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  "backup_version": "1.0",
  "exported_at": "2026-11-09T00:22:06Z",
  "total_articles": 7,
  "articles": [
    {
      "title": "mnnnnn b",
      "authors": [],
      "affiliations": [],
      "corr_author": "",
      "corr_email": "",
      "abstract": "\\section{} Microplastics (plastic particles smaller than 5 mm) are among the most widespread environmental pollutants, and monitoring them requires both counting particles and identifying their polymer type. Spectroscopic methods such as FTIR and Raman are accurate but slow and costly. Nile Red staining offers a fast, inexpensive alternative, as stained plastics fluoresce under blue light, but turning fluorescence images into quantitative data requires reliable automated detection and classification. We used the public Nile Red dataset of Rermborirak et al. (2025), covering six polymer classes (ABS, Nylon, PE, PET, PS and PVC). A systematic audit found that 1,012 of the 2,566 published images (39.4%) were near-duplicates, many with bounding-box labels rotated by 180\u00b0. After de-duplication, 1,554 unique images (23,832 labelled particles) were split 70/15/15 into training, validation and test sets, stratified by polymer class. Five YOLO detectors (YOLOv8s, YOLOv9s, YOLOv10s, YOLO11s and YOLO26s) were trained for 60 epochs at 640 pixels from COCO-pretrained weights, all with identical hyperparameters. The best architecture, YOLO26s, was then fine-tuned for 100 further epochs at 640 and 960 pixels, with model selection based on validation performance only. Evaluation combined standard detection metrics with an independent error analysis separating located, misclassified, missed and spurious particles. YOLO26s, YOLO11s and YOLOv10s performed equivalently (test mAP50-95 0.822\u20130.828), about 3 points above YOLOv8s (0.795), the architecture used in the source study. The final YOLO26s model, fine-tuned at 960 pixels, achieved test precision 0.909, recall 0.904, mAP50 0.962 and mAP50-95 0.876, a gain of 8.1 points over YOLOv8s. At a confidence threshold of 0.25 it located 96.0% of labelled particles, and only 0.5\\ a threshold of 0.50 it counted particles with a mean absolute error of 1.46 per image. The accuracy gain splits roughly equally between newer architecture (+2.8 points), longer training (+2.4) and higher input resolution (+2.9). Polymer classification of located particles is effectively solved; the main remaining challenge is spurious detection of faint, unannotated particles. The model, code and methodology are released for reproducibility.",
      "keywords": "Microplastics, Nile Red fluorescence, object detection, YOLO26, deep learning, polymer classification, fluorescence microscopy, environmental monitoring",
      "doi": "10.3389/feduc.2026.8255139",
      "article_url_path": "/journals/education/articles/10.3320/feduc.2026.82975539/abstract",
      "journal_slug": "education",
      "journal": "Frontiers in Education",
      "journal_abbrev": "Front. Educ.",
      "section": "Sec. Higher Education",
      "banner": "/assets/images/journals/education-banner.png",
      "issn": "2504-284X",
      "impact_factor": "2.6",
      "citescore": "4.3",
      "received": "2026-03-12",
      "accepted": "2026-11-01",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
      "views_count": "10",
      "demographics": [
        {
          "name": "United States",
          "views": 6
        },
        {
          "name": "India",
          "views": 4
        }
      ],
      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% This is just an example/guide for you to refer to when submitting manuscripts to Frontiers, it is not mandatory to use Frontiers .cls files nor frontiers.tex  %\n% This will only generate the Manuscript, the final article will be typeset by Frontiers after acceptance.   \n%                                              %\n%                                                                                                                                                         %\n% When submitting your files, remember to upload this *tex file, the pdf generated with it, the *bib file (if bibliography is not within the *tex) and all the figures.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%% Version 3.4 Generated 2022/06/14 %%%\n%%% You will need to have the following packages installed: datetime, fmtcount, etoolbox, fcprefix, which are normally inlcuded in WinEdt. %%%\n%%% In http://www.ctan.org/ you can find the packages and how to install them, if necessary. %%%\n%%%  NB logo1.jpg is required in the path in order to correctly compile front page header %%%\n\n\\documentclass[utf8]{FrontiersinHarvard} % for articles in journals using the Harvard Referencing Style (Author-Date), for Frontiers Reference Styles by Journal: https://zendesk.frontiersin.org/hc/en-us/articles/360017860337-Frontiers-Reference-Styles-by-Journal\n%\\documentclass[utf8]{FrontiersinVancouver} % for articles in journals using the Vancouver Reference Style (Numbered), for Frontiers Reference Styles by Journal: https://zendesk.frontiersin.org/hc/en-us/articles/360017860337-Frontiers-Reference-Styles-by-Journal\n%\\documentclass[utf8]{frontiersinFPHY_FAMS} % Vancouver Reference Style (Numbered) for articles in the journals \"Frontiers in Physics\" and \"Frontiers in Applied Mathematics and Statistics\" \n\n%\\setcitestyle{square} % for articles in the journals \"Frontiers in Physics\" and \"Frontiers in Applied Mathematics and Statistics\" \n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\n% Additional packages required by this manuscript (equations and tables)\n\\usepackage{amsmath,amssymb}\n\\usepackage{tabularx}\n\\usepackage{placeins}\n\\newcolumntype{C}{>{\\centering\\arraybackslash}X}\n\\newcolumntype{L}{>{\\raggedright\\arraybackslash}X}\n\\newcolumntype{P}[1]{>{\\raggedright\\arraybackslash}p{#1}}\n\n\\linenumbers\n\n\n% Leave a blank line between paragraphs instead of using \\\\\n\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\n\n\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title {Fine-Tuned YOLO26 for Automated Detection and Polymer Classification of Microplastics in Nile Red Fluorescence Microscopy Images} \n\n\\author[\\firstAuthorLast ]{\\Authors} %This field will be automatically populated\n\\address{} %This field will be automatically populated\n\\correspondance{} %This field will be automatically populated\n\n\\extraAuth{}% If there are more than 1 corresponding author, comment this line and uncomment the next one.\n%\\extraAuth{corresponding Author2 \\\\ Laboratory X2, Institute X2, Department X2, Organization X2, Street X2, City X2 , State XX2 (only USA, Canada and Australia), Zip Code2, X2 Country X2, email2@uni2.edu}\n\n\n\\maketitle\n\n\n\\begin{abstract}\n\n%%% Leave the Abstract empty if your article does not require one, please see the Summary Table for full details.\n\\section{}\nMicroplastics (plastic particles smaller than 5 mm) are among the most widespread environmental pollutants, and monitoring them requires both counting particles and identifying their polymer type. Spectroscopic methods such as FTIR and Raman are accurate but slow and costly. Nile Red staining offers a fast, inexpensive alternative, as stained plastics fluoresce under blue light, but turning fluorescence images into quantitative data requires reliable automated detection and classification. We used the public Nile Red dataset of Rermborirak et al. (2025), covering six polymer classes (ABS, Nylon, PE, PET, PS and PVC). A systematic audit found that 1,012 of the 2,566 published images (39.4\\%) were near-duplicates, many with bounding-box labels rotated by 180\u00b0. After de-duplication, 1,554 unique images (23,832 labelled particles) were split 70/15/15 into training, validation and test sets, stratified by polymer class. Five YOLO detectors (YOLOv8s, YOLOv9s, YOLOv10s, YOLO11s and YOLO26s) were trained for 60 epochs at 640 pixels from COCO-pretrained weights, all with identical hyperparameters. The best architecture, YOLO26s, was then fine-tuned for 100 further epochs at 640 and 960 pixels, with model selection based on validation performance only. Evaluation combined standard detection metrics with an independent error analysis separating located, misclassified, missed and spurious particles. YOLO26s, YOLO11s and YOLOv10s performed equivalently (test mAP50-95 0.822\u20130.828), about 3 points above YOLOv8s (0.795), the architecture used in the source study. The final YOLO26s model, fine-tuned at 960 pixels, achieved test precision 0.909, recall 0.904, mAP50 0.962 and mAP50-95 0.876, a gain of 8.1 points over YOLOv8s. At a confidence threshold of 0.25 it located 96.0\\% of labelled particles, and only 0.5\\ a threshold of 0.50 it counted particles with a mean absolute error of 1.46 per image. The accuracy gain splits roughly equally between newer architecture (+2.8 points), longer training (+2.4) and higher input resolution (+2.9). Polymer classification of located particles is effectively solved; the main remaining challenge is spurious detection of faint, unannotated particles. The model, code and methodology are released for reproducibility.\n\n\n\\tiny\n \\keyFont{ \\section{Keywords:} Microplastics, Nile Red fluorescence, object detection, YOLO26, deep learning, polymer classification, fluorescence microscopy, environmental monitoring} %All article types: you may provide up to 8 keywords; at least 5 are mandatory.\n % Keywords from the original manuscript not included due to the 8-keyword limit: computer vision, transfer learning, dataset quality, mAP\n\\end{abstract}\n\n\\section{Introduction}\n\\label{sec:introduction}\n\n\\subsection{The Microplastic Pollution Crisis and the Need for High-Throughput Analysis}\n\nMicroplastic particles are plastic fragments, fibres, pellets, films and foams smaller than 5~mm in at least one dimension and as small as 1~$\\mu$m, and have been found in virtually all compartments of the global environment, including deep-sea sediments and Arctic permafrost, drinking water and even human placental tissue. Evidence in epidemiology and toxicology is growing that chronic, low-level exposure to microplastic can lead to disruption of endocrine signalling, inflammatory responses and be vectors for persistent organic pollutants that adsorb to particle surfaces. Standardised, cost-effective and scalable analytical workflows are not yet available, and regulatory bodies around the world are taking action with new monitoring requirements.\n\nCharacterisation of an environmental microplastic sample involves answering two types of questions for each particle: What are the particle's dimensions and where is it found?; and What is the polymer type of the particle? The first question is used to guide exposure assessments and mass-balance models; the second question is used to guide source attribution, persistence modelling and risk characterisation. The simultaneous measurement of both the questions (for hundreds or thousands of particles per sample) at throughputs compatible with routine environmental monitoring is an unsolved analytical challenge.\n\nExisting analytical methods involve isolating particles under white-light microscopy and identifying the polymer in the particles by Fourier-transform infrared (FTIR) or Raman spectroscopy. Both spectroscopic techniques are very specific and capable of characterizing polymer identity with a high degree of confidence; however, the particle needs to be interrogated individually resulting in throughput that is greatly dependent on the particle density. A large-scale monitoring programme may have a severe bottleneck, as a sample of 500 particles per filter could take 4--8 hours of manual spectroscopic analysis per filter.\n\n\\subsection{Nile Red Fluorescence as a High-Throughput Screening Modality}\n\nNile Red (9-Diethylamino-5H-benzo[$\\alpha$]phenoxazin-5-one, CAS 7385-67-3) is a fluorescent dye that was initially designed as a stain for lipids and is also a solvatochromic dye. Its amphiphilic nature, consisting of a hydrophobic benzophenoxazine backbone and an electron donating diethylamino group, allows it to partition preferably into nonpolar environments, such as the surfaces and interiors of hydrophobic polymer particles. NR-stained plastic particles produce fluorescence in the yellow-orange region of the spectrum ($\\lambda_{\\mathrm{em}}$ up to approx.\\ 520--570~nm for highly hydrophobic polymers, e.g.\\ PE; up to approx.\\ 550--620~nm for more polar polymers, e.g.\\ PET) when exposed to UV and blue light (typical $\\lambda_{\\mathrm{ex}}$ approx.\\ 488~nm), while biological organic matter and mineral particles (which are poorly stained or not stained at all) are comparatively faint under the same exposure conditions.\n\nThe use of the emission wavelength of NR stained particles has been shown to provide the information necessary for coarse polymer discrimination along with particle morphology by several groups. The NR staining method has been previously demonstrated to be able to detect microplastics in field samples rapidly and quantify them \\citep{shim2016}, as well as to detect particles as small as 1--20~$\\mu$m \\citep{erni2017} and for rapid screening of field samples \\citep{maes2017}. Importantly, NR staining and fluorescence imaging can be carried out with simple laboratory equipment, a standard epifluorescence microscope or even a smartphone coupled to an optical filter, and is therefore suitable for use in less well-equipped environments and for field deployable monitoring platforms.\n\nThis was extended to a fully portable monitoring system by \\citet{rermborirak2025}, where NR staining was coupled with YOLOv8 deep learning object detector trained on a new publicly available dataset of NR fluorescence images of six polymer classes. They present their system, which shows the feasibility of simultaneous particle localisation and polymer identification from single fluorescence images, both of which can be automated. This paper directly leverages their data to evaluate if there is a significant improvement in the detection accuracy using more recent YOLO architectures, longer training periods and higher input resolution for the predict phase.\n\n\\subsection{Object Detection with YOLO-Family Architectures}\n\nYOLO architectures are a family of anchor-free (in recent generations), single-stage object detection approaches that process a whole image in a single forward pass through a CNN, and output a class probability and the coordinates of a bounding box at once. The design of the architecture has been undergoing a quick series of successive improvements since its inception in the original YOLO paper \\citep{redmon2016}, where every generation has transformed the backbone design, the feature pyramid, the loss function, and the training strategy.\n\nYOLOv8 family \\citep{jocher2023yolov8} presented a fully decoupled head, an anchor-free detection, and a distributional focal loss (DFL) box regression formulation. YOLOv9 \\citep{wang2024yolov9} presented programmable gradient information (PGI) and a generalised efficient layer aggregation network (GELAN). \\citet{wang2024yolov10} and \\citet{jocher2026yolo26} independently proposed YOLOv10 and YOLO26, respectively, which are NMS-free end-to-end detectors that are trained using dual-assignment: a one-to-many head with multiple assignments per ground truth box offers a strong training objective, and a one-to-one head learns to suppress duplicated predictions, eliminating NMS at inference and making deployment pipelines easier. YOLO11 \\citep{jocher2024yolo11} improved the C3k2 feature block and added the position-sensitive self-attention module (C2PSA). YOLO26 builds on this design by providing small-target-aware label assignment, progressive dual-head loss weighting, and further attention at the neck-level.\n\nAll three classic YOLO failure modes -- small object detection failure, coarse box failure and failure to differentiate between spectrally similar polymer classes -- are directly relevant to the task of microplastic detection in these architectural innovations.\n\n\\subsection{Aims and Contributions}\n\nThe present work pursues a single overarching aim: \\textbf{to produce and publicly document the most accurate object detector achievable on the \\citet{rermborirak2025} dataset within the constraints of a consumer-grade GPU (NVIDIA GeForce RTX 3050, 6~GB VRAM), and to decompose the accuracy gain into its constituent sources.} The concrete contributions are:\n\n\\begin{itemize}\n\\item A reproducible dataset quality audit, identifying and resolving a large-scale duplication and label-rotation defect in the source dataset.\n\\item A controlled multi-architecture benchmark comparing five YOLO families under identical training conditions.\n\\item A fine-tuning campaign that identifies extended training duration and enlarged input resolution as independent, approximately equal sources of accuracy improvement.\n\\item An independent, framework-agnostic error-analysis methodology that disentangles localisation errors, classification errors, missed particles, and spurious detections.\n\\item A deployment-ready model card with recommended confidence-threshold guidance for two distinct operational modes: maximum-recall screening and minimum-error counting.\n\\end{itemize}\n\n\\FloatBarrier\n\\section{Literature Review}\n\\label{sec:literature}\n\n\\subsection{Environmental presence and toxicity of micro-plastics}\n\n% NOTE: the original manuscript cites \"Thompson et al. (2004)\" here, but its reference list only contains Thompson et al. (2009), \"Our plastic age\". Please check and replace with \\citet{...} once resolved.\nThe scientific publications on the topic of microplastic contamination have grown exponentially since the invention of the term by Thompson et al. (2004). The presence of microplastics has been reported in marine invertebrates, fish, seabirds and marine mammals. Microplastics have been found in the lungs, blood, colon tissue and placentae of humans. model organism toxicological studies have shown to produce oxidative stress, inflammation, changes in gene expression, developmental abnormalities and trophic transfer. The type of polymer makes a significant difference in the toxicological outcome; polyvinyl chloride (PVC) and polystyrene (PS) particles are more likely to be more cytotoxic than polyethylene (PE) or polypropylene (PP) particles due in part to additive leaching and differences in surface chemistry. This polymer dependence highlights the need to identify microplastics as well as detect them in analysis.\n\n\\subsection{Classical Analytical Methods}\n\nThe gold standard for polymer identification is FTIR spectroscopy, both ATR for particles $\\geq$ 500~$\\mu$m and focal-plane array $\\mu$FTIR for smaller particles, which may be unambiguously assigned from a spectral library match against reference spectra. But for a high-density filter, the time for $\\mu$FTIR mapping can be 30--90 minutes per sample (excluding sample preparation). Raman spectroscopy, which also encompasses surface-enhanced Raman spectroscopy (SERS), has comparable selectivity with higher spatial resolution ($>$ 1 micron), but has similar throughput restrictions and is also subject to interference from organic matter by fluorescence. Pyrolysis-gas chromatography--mass spectrometry (Py-GC/MS) is one technique that allows the quantification of bulk polymer in complex samples without achieving individual particle resolution. All of these approaches are not easily expandable to the volumes of soil samples necessary for routine large-scale soil monitoring.\n\n\\subsection{Fluorescence-Based Screening Methods}\n\nAs an additional rapid screening method, fluorescent dyes selective for plastic polymers were pioneered in the mid 2010s. The Nile Red, which was the first stain to be used in the field of microplastics by \\citet{shim2016}, was followed by other stains such as fluorescein diacetate (FDA), calcofluor white (CFW, used to exclude cellulose fibres), and excitation-emission matrix fluorescence spectroscopy approaches. NR has been the most popular choice due to its high polymer selectivity, user-friendly and compatibility with the standard fluorescence microscope and even smartphone based readers.\n\nSeveral shortcomings have been identified by critical evaluations of NR staining: incompleteness of staining polar polymers (PET, nylon), false-positive of NR-retaining biological particles (some algae, wax particles) and variation in dye concentration between different batches. It has been demonstrated that these artefacts can be significantly reduced by standardisation of NR concentration, staining time and rinsing protocol. Further automation of image analysis of NR-stained samples was based on simple thresholding and watershed-based segmentation, which work well for isolated particles but are not effective at high particle densities and for morphologically complicated aggregates. These methods rely on classification.\n\n\\subsection{Classification based methods for microplastic detection by deep learning}\n\nThe first use of deep convolutional neural networks (CNNs) for the detection and classification of microplastics is in bright-field and scanning electron microscopy (SEM) images, where transfer learning is employed from ImageNet-pretrained feature extractors that allows for accurate polymer discrimination using only a small training set. New challenges were introduced when translating to NR fluorescence images: the images are only single channel/pseudo-colour, the particles boundaries are soft and the background fluorescence is variable.\n\n% NOTE: \"Kershaw et al. (2023)\" is cited in the original manuscript but does not appear in its reference list. Please add a test.bib entry and replace with \\citet{...}.\nKershaw et al. (2023) showed CNN models could be used to classify isolated NR stained microplastic particles from images of the crop with accuracy $>$90\\% for six different polymer classes. The first systematic study of end-to-end object detection (localisation and classification of particles without prior isolation) was carried out by \\citet{rermborirak2025}, who trained YOLOv8 on their NR dataset and achieved high accuracy according to their test procedure. This work is the first multi-architecture comparative study on this dataset and the first systematic fine-tuning campaign on this dataset with regards to both training duration and input resolution. However, for small-object detection, the YOLO architecture has been evolved by the following strategies:\n\n\\subsection{YOLO Architecture Evolution Relevant to Small-Object Detection}\n\nThis difficulty in detecting small objects has led to many architectural innovations in the YOLO family that occupy less than 32$\\times$32 pixels at standard detection-head resolution. In YOLOv4, high-resolution feature maps at the finest detection scale can be fused with semantic information that is passed up from deeper and more semantically rich layers through the use of feature pyramid networks (FPNs) and path aggregation networks (PANs) introduced in the model and further refined. Anchor-free methods, like those used in FCOS and subsequently inherited by YOLOv8 and its descendants, eliminate the need for anchor-based method to match the size of objects in the data set and enhance generalization.\n\nTo capture long-range spatial dependencies, self-attention mechanisms (Yolov11: C2PSA; Yolov26: C2PSA + neck attention) have been integrated into the backbone of YOLO. In dense scenes, like the microplastic images, where it is possible that the particles affect each other in their fluorescence background, theoretically it is beneficial to use attention-based context aggregation. While evidence from the present benchmark, which is based on empirical results, is consistent with this hypothesis, it is not possible to make causal claims given the co-occurrence of different feature blocks and training algorithms between the attention equipped and attention free architectures (e.g.\\ YOLO26s, YOLO11s vs YOLOv8s and YOLOv9s).\n\nThe NMS-free dual-assignment paradigm has been proposed in YOLOv10 and YOLO26 to overcome another type of failure, which is the prediction of duplicate predictions. In dense detection situations, NMS may be able to remove true particles in high density aggregates that are close together in location. End-to-end detectors with a one-to-one assignment constraint learn to make only one box for each particle, which alleviates this failure mode and shortens the subsequent post-processing pipeline. This design intent is reflected in the present error analysis, which shows a decrease in the number of extra boxes for both the YOLO26s and YOLOv10s.\n\n\\subsection{Transfer Learning and Fine-Tuning Strategies for Scientific Imaging}\n\nThe domain shift between large-scale natural-image datasets (ImageNet, COCO) and scientific image datasets is particularly strong for fluorescence microscopy: the statistics of the features in pseudo-colour fluorescence images are very different from the statistics of natural photos; also, the objects of interest (sub-100-pixel fluorescent particles, on a dark background) do not look anything like the natural objects that the feature extractors were trained on. Even though of this change, transfer learning from COCO-pretrained weights always performs better than training from random initialisation in the size of ranges of the fluorescence datasets typical to scientific imaging (hundreds to low thousands), because the general low-level features learned by the pretrained backbone (edge detectors, colour contrasts) can be transferred across domain with usefulness.\n\nTypical fine tuning strategies for scientific imaging datasets include: (1) starting with a small learning rate to allow the pretrained features to adapt slowly; (2) augmentation to the domain -- for NR fluorescence images, a large color augmentation is useful, because the intensity of the image can vary from the dye concentration and illumination, whereas large geometric distortions have to be used with care because some polymer types are morphologically distinct; and (3) scaling of the input resolution, especially when the native resolution of the images is higher than the resolution of the images used in training, and small targets are present.\n\n\\FloatBarrier\n\\section{Dataset}\n\\label{sec:dataset}\n\n\\subsection{Source Dataset}\n\nThe dataset released by \\citet{rermborirak2025}, available at \\url{https://github.com/sombsuk/dataset_microplastic}, contains fluorescence micrographs of Nile Red-stained plastic particles for six polymer classes: acrylonitrile butadiene styrene (ABS), Nylon (polyamide), polyethylene (PE), polyethylene terephthalate (PET), polystyrene (PS), and polyvinyl chloride (PVC). Each image contains particles of a single polymer type, and each particle is annotated with a bounding box in YOLO format (class index, normalised centre x, normalised centre y, normalised width, normalised height). The as-published corpus comprises 2,566 images with 38,841 labelled particles, distributed across the six classes as shown in Table~\\ref{tab:dataset_published}.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Contents of the dataset as published by \\citet{rermborirak2025}. ABS = acrylonitrile butadiene styrene; PE = polyethylene; PET = polyethylene terephthalate; PS = polystyrene; PVC = polyvinyl chloride.}\n\\label{tab:dataset_published}\n\\begin{tabularx}{\\linewidth}{l C C C L}\n\\hline\n\\textbf{Polymer} & \\textbf{Images (published)} & \\textbf{Labelled particles} & \\textbf{Particles / image (mean)} & \\textbf{Image resolutions present} \\\\\n\\hline\nABS   & 406   & 3,944  & 9.7  & 640$\\times$480, 1280$\\times$960 \\\\\nNylon & 592   & 7,067  & 11.9 & 640$\\times$480, 780$\\times$585 \\\\\nPE    & 496   & 15,999 & 32.3 & 640$\\times$480, 1280$\\times$960, 742$\\times$556 \\\\\nPET   & 272   & 710    & 2.6  & 640$\\times$480 \\\\\nPS    & 272   & 1,784  & 6.6  & 640$\\times$480, 780$\\times$585 \\\\\nPVC   & 528   & 9,337  & 17.7 & 640$\\times$480, 780$\\times$585 \\\\\n\\hline\nTotal & 2,566 & 38,841 & 15.1 & Multiple (4:3 ratio) \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\subsection{Data Audit}\n\nBefore any model training, a systematic quality audit of the raw dataset was performed. The audit comprised the following checks: (1) image--label pairing completeness; (2) label format validity; (3) class-index consistency; (4) exact duplicate detection by MD5 hash; (5) near-duplicate detection by 256-bit perceptual difference hash (dHash) with a Hamming distance threshold of 12 bits; and (6) label-alignment scoring by comparing the mean fluorescence intensity inside labelled bounding boxes versus the background.\n\nThe dHash algorithm computes a perceptual fingerprint of an image by resizing it to a 17$\\times$16 grayscale patch and encoding whether each pixel in each row is brighter than its right neighbour, producing a 256-bit bitstring. The Hamming distance between two such hashes---the number of bit positions that differ---provides a measure of visual similarity that is invariant to minor rendering or compression differences. The threshold of 12 bits was chosen by inspection of the distance distribution, which shows a bimodal distribution with a clear gap between near-zero distances (duplicate pairs) and distances above 50 (distinct images).\n\nThe label-alignment score for a given image with label set $L$ is defined as:\n\\begin{equation}\nS_{\\mathrm{align}} = \\bar{I}_{\\mathrm{inside}}(L) - \\bar{I}_{\\mathrm{outside}}(L)\n\\label{eq:align}\n\\end{equation}\nwhere $\\bar{I}_{\\mathrm{inside}}(L)$ is the mean normalised fluorescence intensity within all labelled bounding boxes and $\\bar{I}_{\\mathrm{outside}}(L)$ is the mean normalised fluorescence intensity in the complement region. A positive $S_{\\mathrm{align}}$ indicates that the labels correctly delineate brighter regions; a strongly positive $S_{\\mathrm{align}}$ after 180$^{\\circ}$ rotation of the label coordinates but not the image indicates that the labels were erroneously rotated relative to the image. The rotation transforms each label coordinate $(x, y) \\rightarrow (1-x, 1-y)$.\n\nThe audit found 1,020 near-duplicate pairs. In 967 of these pairs, exactly one copy carries labels that fit the image significantly better after 180$^{\\circ}$ rotation ($S_{\\mathrm{align}}(\\mathrm{rot}) - S_{\\mathrm{align}}(\\mathrm{orig}) > 0.10$). Cross-matching labels between the two copies of each pair confirms the defect: as published, only 2.7\\% of boxes in one copy match a box in the other at IoU $\\geq$ 0.5; after applying the 180$^{\\circ}$ rotation correction, 97.9\\% match.\n\n\\subsection{Cleaned Dataset and Split}\n\nDe-duplication was performed by grouping images within each polymer class whose dHash distances fall below the 12-bit threshold (union-find algorithm), selecting the representative of each group as the copy whose published labels fit the image without rotation (minimum $S_{\\mathrm{align}}(\\mathrm{rot}) - S_{\\mathrm{align}}(\\mathrm{orig})$, preferring high absolute $S_{\\mathrm{align}}$). After de-duplication, 1,554 unique frames remained; none required label rotation, confirming that the defect was confined to the duplicated copies.\n\nThe 1,554 unique frames were divided into training, validation, and test subsets in a 70/15/15 ratio, stratified by polymer class, with a fixed random seed (seed = 0) to ensure exact reproducibility. Stratification ensures that the class distribution is approximately preserved across subsets. The split is performed at the level of unique frames, guaranteeing that no particle image contributes to more than one subset.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Cleaned and split dataset. Images in the validation and test sets are distinct unique fluorescence frames.}\n\\label{tab:dataset_split}\n\\begin{tabularx}{\\linewidth}{l C C C C C C}\n\\hline\n\\textbf{Polymer} & \\textbf{Train images} & \\textbf{Train particles} & \\textbf{Val images} & \\textbf{Val particles} & \\textbf{Test images} & \\textbf{Test particles} \\\\\n\\hline\nABS   & 178   & 1,619  & 38  & 429   & 38  & 338 \\\\\nNylon & 258   & 3,173  & 56  & 691   & 56  & 668 \\\\\nPE    & 190   & 6,323  & 41  & 1,317 & 41  & 1,354 \\\\\nPET   & 113   & 343    & 24  & 79    & 24  & 66 \\\\\nPS    & 112   & 785    & 24  & 175   & 24  & 160 \\\\\nPVC   & 235   & 4,548  & 51  & 944   & 51  & 820 \\\\\n\\hline\nTotal & 1,086 & 16,791 & 234 & 3,635 & 234 & 3,406 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\section{Methodology}\n\\label{sec:methodology}\n\n\\subsection{Overview of the Experimental Pipeline}\n\nThe experimental pipeline comprised four sequential phases: (1) dataset preparation and quality control (Section~\\ref{sec:dataset}); (2) multi-architecture benchmark training and evaluation; (3) fine-tuning of the selected architecture at two input resolutions; and (4) independent error analysis of the benchmark and final models. Each phase is described in detail in the subsections below.\n\n\\subsection{Model Architectures}\n\nFive YOLO-family architectures were selected for the benchmark, all at the small (``s'') size tier to control for model capacity and ensure that performance differences reflect architectural design rather than parameter count. All models were initialised from publicly available weights pretrained on the Microsoft COCO 2017 object detection benchmark \\citep{lin2014coco}, which contains 118,000 training images with bounding-box annotations for 80 object categories.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Benchmark architectures. GFLOPs = giga floating-point operations at 640-pixel input. DFL = distribution focal loss; GELAN = generalised efficient layer aggregation network; SCDown = spatially channel-separated downsampling; C2fCIB = compact inverted bottleneck block; C2PSA = position-sensitive self-attention.}\n\\label{tab:architectures}\n\\begin{tabularx}{\\linewidth}{l l >{\\centering\\arraybackslash}p{1.9cm} >{\\centering\\arraybackslash}p{1.9cm} L}\n\\hline\n\\textbf{Architecture} & \\textbf{Reference} & \\textbf{Parameters (M)} & \\textbf{GFLOPs at 640 px} & \\textbf{Key innovations} \\\\\n\\hline\nYOLOv8s  & \\citet{jocher2023yolov8} & 11.1 & 28.7 & Decoupled head; anchor-free; DFL box regression \\\\\nYOLOv9s  & \\citet{wang2024yolov9}   & 7.3  & 27.4 & Programmable gradient info; GELAN feature block \\\\\nYOLOv10s & \\citet{wang2024yolov10}  & 8.1  & 24.9 & NMS-free dual assignment; SCDown; C2fCIB block \\\\\nYOLO11s  & \\citet{jocher2024yolo11} & 9.4  & 21.7 & C3k2 block; C2PSA self-attention; lightweight class head \\\\\nYOLO26s  & \\citet{jocher2026yolo26} & 10.0 & 22.8 & NMS-free; C3k2; C2PSA + neck attention; direct box regression; small-target assignment \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\subsection{Training Configuration}\n\nAll benchmark models were trained with rigorously identical hyperparameters to isolate the effect of architecture. The configuration is summarised in Table~\\ref{tab:hyperparameters}. The learning-rate schedule follows a linear warm-up followed by linear decay, as formalised by:\n\\begin{equation}\n\\eta(t) = \\eta_0 \\times\n\\begin{cases}\nt/t_{\\mathrm{warm}} & \\text{if } t \\leq t_{\\mathrm{warm}}\\\\[4pt]\n1 - (1 - \\eta_f/\\eta_0) \\times (t - t_{\\mathrm{warm}})/(T - t_{\\mathrm{warm}}) & \\text{if } t > t_{\\mathrm{warm}}\n\\end{cases}\n\\label{eq:lr_linear}\n\\end{equation}\nwhere $\\eta_0 = 0.001$ is the initial learning rate, $\\eta_f = 0.00001$ is the final learning rate ($\\eta_f/\\eta_0 = 0.01$), $t_{\\mathrm{warm}} = 3$ epochs is the warm-up duration, and $T = 60$ epochs is the total training duration.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Training hyperparameters, identical for all benchmark models.}\n\\label{tab:hyperparameters}\n\\begin{tabularx}{\\linewidth}{P{3.2cm} L L}\n\\hline\n\\textbf{Hyperparameter} & \\textbf{Value} & \\textbf{Rationale} \\\\\n\\hline\nPretrained weights & COCO 2017 & Initialises feature extractors from a large general-purpose dataset \\\\\nTotal epochs & 60 (early stopping: patience = 25) & All models were still improving at epoch 60; no early stopping triggered \\\\\nInput resolution & 640 $\\times$ 640 pixels (letterboxed) & Matches pretrained input; baseline resolution \\\\\nBatch size & 16 & Maximum feasible for 6 GB VRAM at this resolution \\\\\nOptimiser & AdamW \\citep{loshchilov2019} & Auto-selected by Ultralytics; $\\beta_1 = 0.9$, $\\beta_2 = 0.999$, $\\epsilon = 1\\times10^{-8}$, $\\lambda = 5\\times10^{-4}$ \\\\\nLearning rate & $\\eta_0 = 0.001$, $\\eta_f = 0.00001$ & Linear warm-up (3 epochs) + linear decay \\\\\nMixed precision & Automatic (FP16/FP32) & Reduces VRAM requirement; no accuracy impact \\\\\nMosaic augmentation & On for epochs 1--50; off for 51--60 & Disabled at end of training to stabilise fine-grained features \\\\\nGeometric augmentation & Scale $\\pm$50\\%; translate $\\pm$10\\%; h-flip $p = 0.5$; v-flip $p = 0.5$ & v-flip added: microscope images lack natural orientation \\\\\nColour augmentation & Hue $\\pm$1.5\\%; saturation $\\pm$70\\%; brightness $\\pm$40\\% & Models fluorescence intensity variation across staining batches \\\\\nLoss weights & Box: 7.5; class: 0.5; DFL: 1.5 & Ultralytics defaults; emphasis on localisation accuracy \\\\\nRandom seed & 0 & Ensures reproducibility \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nThe composite training loss $L_{\\mathrm{train}}$ for each model is:\n\\begin{equation}\nL_{\\mathrm{train}} = w_{\\mathrm{box}} \\times L_{\\mathrm{box}} + w_{\\mathrm{cls}} \\times L_{\\mathrm{cls}} + w_{\\mathrm{dfl}} \\times L_{\\mathrm{dfl}}\n\\label{eq:loss_total}\n\\end{equation}\nwhere $L_{\\mathrm{box}}$ is the Complete IoU (CIoU) regression loss, $L_{\\mathrm{cls}}$ is the binary cross-entropy classification loss, and $L_{\\mathrm{dfl}}$ is the distribution focal loss applied to the predicted edge-distribution logits. The weights are $w_{\\mathrm{box}} = 7.5$, $w_{\\mathrm{cls}} = 0.5$, and $w_{\\mathrm{dfl}} = 1.5$.\n\nThe CIoU loss penalises not only the IoU between predicted box $\\hat{B}$ and ground-truth box $B$, but also the aspect ratio inconsistency and centre-distance normalised by the enclosing box diagonal:\n\\begin{equation}\nL_{\\mathrm{CIoU}} = 1 - \\mathrm{IoU}(\\hat{B}, B) + \\rho^{2}(\\hat{b}, b)/c^{2} + \\alpha \\times v\n\\label{eq:ciou}\n\\end{equation}\nwhere $\\rho(\\hat{b}, b)$ is the Euclidean distance between the centres of $\\hat{B}$ and $B$, $c$ is the diagonal of the smallest enclosing box, $v = (4/\\pi^{2})\\left(\\arctan(w/h) - \\arctan(\\hat{w}/\\hat{h})\\right)^{2}$ penalises aspect-ratio inconsistency, and $\\alpha = v/(1 - \\mathrm{IoU} + v)$ weights the aspect-ratio term adaptively.\n\nThe distribution focal loss, introduced in \\citet{tian2020fcos} and adopted from FCOS-based regression, models each box edge offset $\\Delta$ as a discrete probability distribution $P$ over a set of $n$ bins $\\{0, 1, \\ldots, n-1\\}$ (with $n = 16$ for DFL-based models; $n = 1$ for YOLO26 which regresses directly):\n\\begin{equation}\nL_{\\mathrm{DFL}} = -\\sum_{i} \\Big[ (y_0 - i) \\times \\log P(i) \\times \\mathbf{1}[i = \\lfloor y \\rfloor] + (i - y_0) \\times \\log P(i) \\times \\mathbf{1}[i = \\lceil y \\rceil] \\Big]\n\\label{eq:dfl}\n\\end{equation}\nwhere $y_0$ is the continuous true offset and $\\mathbf{1}[\\cdot]$ is the indicator function. This formulation encourages the model to concentrate its prediction probability mass on the two bins flanking the true offset, enabling subpixel localisation accuracy.\n\n\\FloatBarrier\n\\subsection{Label Assignment Strategy}\n\nDuring training, the task-aligned assigner (TAL) is used to determine which anchor points are responsible for predicting each ground-truth box. TAL scores each anchor point $k$ relative to each ground-truth box $g$ by:\n\\begin{equation}\ns(k, g) = p_{g}(k)^{\\alpha} \\times \\mathrm{IoU}(B_{k}, B_{g})^{\\beta}\n\\label{eq:tal}\n\\end{equation}\nwhere $p_{g}(k)$ is the predicted class probability for class $g$ at anchor $k$, $B_{k}$ is the predicted box at anchor $k$, and $\\alpha$ and $\\beta$ are scaling exponents (typically $\\alpha = 0.5$, $\\beta = 6.0$). The top-$K$ anchor points with the highest alignment scores for each ground-truth box are selected as positives. For YOLO26, anchor points whose predicted box has a side length below 16 pixels are treated as if the side length were 16 pixels during this selection, ensuring that very small ground-truth objects receive sufficient positive assignments.\n\n\\subsection{Fine-Tuning Protocol}\n\nThe fine-tuning phase was initiated from the YOLO26s benchmark checkpoint (\\texttt{best.pt}, epoch 60) in two parallel experimental arms: one continuing at 640-pixel input resolution and one at 960-pixel resolution. The fine-tuning training schedule used the same AdamW optimiser with cosine learning-rate decay:\n\\begin{equation}\n\\eta(t) = \\eta_f + \\tfrac{1}{2}(\\eta_0 - \\eta_f)\\left(1 + \\cos\\left(\\frac{\\pi (t - t_{\\mathrm{warm}})}{T - t_{\\mathrm{warm}}}\\right)\\right)\n\\label{eq:lr_cosine}\n\\end{equation}\nwhere $T = 100$ additional fine-tuning epochs and the remaining symbols are as defined in Equation~\\ref{eq:lr_linear}. Cosine decay, rather than linear decay, was chosen for fine-tuning because it provides a longer period at intermediate learning rates, allowing the model to explore local minima more thoroughly before converging. The batch size for the 960-pixel arm was reduced to 6 to remain within the 6~GB VRAM constraint.\n\nModel selection between the two fine-tuning arms was performed exclusively on the validation mAP50-95, computed on the same 234 validation images used throughout the study. The test set was not consulted until after the final model was selected.\n\n\\subsection{Evaluation Metrics}\n\nTwo complementary evaluation frameworks were employed:\n\n\\textbf{Standard Detection Metrics (Ultralytics Validator).} At a given confidence threshold $\\tau$, each predicted box is classified as a true positive (TP) if it overlaps a ground-truth box of the same polymer class with IoU $\\geq$ 0.5, and as a false positive (FP) otherwise. The precision $P(\\tau) = \\mathrm{TP}/(\\mathrm{TP} + \\mathrm{FP})$ and recall $R(\\tau) = \\mathrm{TP}/(\\mathrm{TP} + \\mathrm{FN})$ are computed as functions of $\\tau$. The average precision AP is the area under the precision-recall curve, estimated by the trapezoidal rule:\n\\begin{equation}\n\\mathrm{AP} = \\int_{0}^{1} P(R)\\,\\mathrm{d}R \\approx \\sum_{n} (R_{n} - R_{n-1}) \\times P_{n}\n\\label{eq:ap}\n\\end{equation}\nThe mean average precision at IoU threshold 0.5 (mAP50) averages AP50 across all polymer classes. The metric mAP50-95 averages AP over IoU thresholds from 0.5 to 0.95 in steps of 0.05, providing a stricter measure that rewards tightly fitting bounding boxes:\n\\begin{equation}\n\\mathrm{mAP50\\text{-}95} = \\frac{1}{10} \\times \\sum_{\\tau \\in \\{0.5,\\, 0.55,\\, \\ldots,\\, 0.95\\}} \\mathrm{mAP}(\\tau)\n\\label{eq:map}\n\\end{equation}\n\n\\textbf{Independent Error Analysis.} Predictions at a fixed confidence threshold $\\tau$ are matched to ground-truth boxes by a greedy algorithm ordered by decreasing prediction confidence. A match is accepted if IoU $\\geq$ 0.5; each ground-truth box can be matched at most once; class labels are ignored during matching to decouple localisation accuracy from classification accuracy. This yields four disjoint outcome categories per particle:\n\n\\begin{itemize}\n\\item Located, correct class (LC): matched to a ground-truth box of the same class.\n\\item Located, incorrect class (LW): matched to a ground-truth box of a different class.\n\\item Missed (FN): ground-truth box with no matching prediction.\n\\item Extra (FP): predicted box that matches no ground-truth box.\n\\end{itemize}\n\nThe per-image count error $\\varepsilon_{i} = \\hat{N}_{i} - N_{i}$ (predicted minus true particle count) is reported as the mean bias $\\mu_{\\varepsilon} = \\mathrm{mean}(\\varepsilon_{i})$ and the mean absolute error $\\mathrm{MAE} = \\mathrm{mean}(|\\varepsilon_{i}|)$. Image-level polymer identification is performed by majority vote over all detections in an image, with ties resolved in favour of the class with the highest mean confidence among its detections.\n\n\\subsection{Intersection over Union (IoU) Formulation}\n\nFor two axis-aligned rectangular boxes $\\hat{B} = (\\hat{x}_{1}, \\hat{y}_{1}, \\hat{x}_{2}, \\hat{y}_{2})$ (predicted) and $B = (x_{1}, y_{1}, x_{2}, y_{2})$ (ground truth), the intersection over union is:\n\\begin{equation}\n\\begin{split}\n\\mathrm{IoU}(\\hat{B}, B) &= \\mathrm{Area}(\\hat{B} \\cap B)/\\mathrm{Area}(\\hat{B} \\cup B)\\\\\n&= \\max\\!\\big(0, \\min(\\hat{x}_{2}, x_{2}) - \\max(\\hat{x}_{1}, x_{1})\\big) \\times \\max\\!\\big(0, \\min(\\hat{y}_{2}, y_{2}) - \\max(\\hat{y}_{1}, y_{1})\\big)\\\\\n&\\quad / \\big(\\mathrm{Area}(\\hat{B}) + \\mathrm{Area}(B) - \\mathrm{Area}(\\hat{B} \\cap B)\\big)\n\\end{split}\n\\label{eq:iou}\n\\end{equation}\nA pair of boxes with IoU $\\geq$ 0.5 is considered a matching pair in both the standard metrics framework and the independent error analysis. The threshold of 0.5 is the conventional ``Pascal VOC'' matching criterion and is used throughout this work unless explicitly stated otherwise.\n\n\\subsection{Image Perceptual Hashing for Duplicate Detection}\n\nThe difference hash (dHash) algorithm was used for near-duplicate detection. For each image $I$, a grayscale thumbnail $G$ of dimensions 17$\\times$16 is computed by bilinear downsampling. The 256-bit hash $h$ is computed as:\n\\begin{equation}\nh[k] = \\mathbf{1}\\big[G[r,c] > G[r,c+1]\\big], \\quad k = 16r + c, \\quad r \\in \\{0, \\ldots, 15\\}, \\quad c \\in \\{0, \\ldots, 15\\}\n\\label{eq:dhash}\n\\end{equation}\nThe Hamming distance $d(h_{i}, h_{j}) = \\sum_{k} h_{i}[k] \\oplus h_{j}[k]$ between any two images $i$ and $j$ counts the number of bit positions that differ. Images within the same polymer class with $d < 12$ were considered near-duplicates; the threshold was validated by manual inspection of 50 randomly sampled pairs across the distance range 0--30.\n\n\\subsection{Hardware and Software Environment}\n\nAll experiments were conducted on a single workstation with an NVIDIA GeForce RTX 3050 GPU (6~GB GDDR6 VRAM), 7.9~GB system RAM, and Windows 11. The software stack consisted of Python 3.14.6, PyTorch 2.11.0 with CUDA 12.8 support, and Ultralytics 8.4.172. The limited system memory required disabling the built-in dataset caching and restricting data-loading workers to at most two. Each completed benchmark model required 27--35 minutes of wall-clock training time.\n\n\\FloatBarrier\n\\section{Results}\n\\label{sec:results}\n\n\\subsection{Benchmark Overview}\n\nTable~\\ref{tab:benchmark} presents the complete benchmark results for five YOLO architectures trained under identical settings on the cleaned microplastic dataset. Results are ordered by validation mAP50-95, the primary model-selection criterion. The test results were computed after training was complete and model selection was finalised; the test set played no role in architecture selection.\n\n\\begin{table}[h!]\n\\centering\n\\footnotesize\n\\setlength{\\tabcolsep}{4pt}\n\\caption{Benchmark results across five YOLO architectures. Models ranked by validation mAP50-95. Best value in each column is underlined. Inference time measured on the NVIDIA RTX 3050 at 640-pixel resolution, single image, batch size 1.}\n\\label{tab:benchmark}\n\\begin{tabularx}{\\linewidth}{l C C C C C C C}\n\\hline\n\\textbf{Model} & \\textbf{Val mAP50} & \\textbf{Val \\mbox{mAP50-95}} & \\textbf{Test Precision} & \\textbf{Test Recall} & \\textbf{Test mAP50} & \\textbf{Test \\mbox{mAP50-95}} & \\textbf{Infer. (ms/img)} \\\\\n\\hline\nYOLO26s  & \\underline{0.956} & \\underline{0.847} & \\underline{0.891} & 0.887 & \\underline{0.944} & 0.823 & 9.7 \\\\\nYOLO11s  & 0.954 & 0.846 & 0.881 & 0.877 & 0.942 & \\underline{0.828} & \\underline{9.4} \\\\\nYOLOv10s & 0.951 & 0.840 & 0.872 & 0.894 & 0.940 & 0.822 & 9.5 \\\\\nYOLOv9s  & 0.938 & 0.815 & 0.844 & \\underline{0.900} & 0.933 & 0.814 & 11.9 \\\\\nYOLOv8s  & 0.929 & 0.812 & 0.851 & 0.864 & 0.916 & 0.795 & \\underline{9.4} \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nThree principal findings emerge from the benchmark:\n\n\\begin{enumerate}\n\\item \\textbf{YOLO26s, YOLO11s, and YOLOv10s are statistically indistinguishable.} The three leading architectures differ by at most 0.7 percentage points on validation mAP50-95 and 0.6 points on test mAP50-95. Given that each model was trained in a single run with a single random seed on a test set of 234 images, the measured differences are within the expected range of run-to-run variance and test-set estimation noise. Model ranking reverses between the validation and test sets (YOLO26s leads on validation; YOLO11s leads on test mAP50-95), which is the characteristic signature of differences that are within noise.\n\\item \\textbf{YOLOv8s is clearly inferior.} YOLOv8s achieves test mAP50-95 of 0.795---approximately 3 percentage points below the three leading architectures, a gap that is consistent across both validation and test sets and across all six polymer classes. This gap reflects a genuine architectural disadvantage, most likely attributable to the absence of self-attention in the YOLOv8s backbone, the full-convolution classification branch, and the less efficient C2f feature block.\n\\item \\textbf{None of the models had converged by epoch 60.} Every model's best checkpoint occurred between epoch 56 and 60, with validation mAP50-95 improving by 0.6 to 2.7 points over the final ten epochs. This demonstrates that the benchmark results represent a lower bound on achievable accuracy for each architecture, and motivates the fine-tuning campaign.\n\\end{enumerate}\n\n\\FloatBarrier\n\\subsection{Per-Polymer Results}\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Test AP50 per polymer class and architecture. ABS remains the most challenging class across all architectures due to its irregular cluster morphology.}\n\\label{tab:per_polymer}\n\\begin{tabularx}{\\linewidth}{l C C C C C}\n\\hline\n\\textbf{Polymer} & \\textbf{YOLO26s AP50} & \\textbf{YOLO11s AP50} & \\textbf{YOLOv10s AP50} & \\textbf{YOLOv9s AP50} & \\textbf{YOLOv8s AP50} \\\\\n\\hline\nABS   & 0.900 & 0.895 & 0.921 & 0.892 & 0.848 \\\\\nNylon & 0.977 & 0.973 & 0.969 & 0.967 & 0.962 \\\\\nPE    & 0.954 & 0.954 & 0.946 & 0.943 & 0.937 \\\\\nPET   & 0.947 & 0.942 & 0.927 & 0.940 & 0.922 \\\\\nPS    & 0.951 & 0.933 & 0.935 & 0.932 & 0.919 \\\\\nPVC   & 0.936 & 0.953 & 0.940 & 0.920 & 0.911 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\subsection{Error Analysis --- Benchmark Models}\n\nTable~\\ref{tab:error_benchmark} presents the independent error analysis at a confidence threshold of 0.25 for all five benchmark models on the 234 test images (3,406 labelled particles, mean 14.6 particles per image).\n\n\\begin{table}[h!]\n\\centering\n\\footnotesize\n\\setlength{\\tabcolsep}{4pt}\n\\caption{Independent error analysis at confidence threshold $\\geq$ 0.25. Count bias = mean (predicted $-$ true) per image; MAE = mean absolute error per image; Image polymer ID = number of test images correctly identified by majority vote over detections.}\n\\label{tab:error_benchmark}\n\\begin{tabularx}{\\linewidth}{l C C C C C C C}\n\\hline\n\\textbf{Model} & \\textbf{Located (\\%)} & \\textbf{Right class (\\%)} & \\textbf{Missed} & \\textbf{Extra boxes} & \\textbf{Count bias/img} & \\textbf{Count MAE/img} & \\textbf{Image polymer ID} \\\\\n\\hline\nYOLO26s  & 95.0\\% & 94.4\\% & 172 & 890   & +3.07 & 3.41 & 232/234 \\\\\nYOLO11s  & 94.8\\% & 93.8\\% & 176 & 908   & +3.13 & 3.52 & 229/234 \\\\\nYOLOv10s & 93.3\\% & 92.6\\% & 227 & 829   & +2.57 & 3.24 & 229/234 \\\\\nYOLOv9s  & 95.8\\% & 95.1\\% & 144 & 1,045 & +3.85 & 3.99 & 232/234 \\\\\nYOLOv8s  & 95.9\\% & 94.2\\% & 141 & 1,136 & +4.25 & 4.39 & 229/234 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\subsection{Final Fine-Tuned Model Results}\n\nFine-tuning YOLO26s from its benchmark checkpoint for 100 additional epochs yielded consistent improvements at both 640-pixel and 960-pixel input resolution. Table~\\ref{tab:finetune} presents the full comparison.\n\n\\begin{table}[h!]\n\\centering\n\\footnotesize\n\\setlength{\\tabcolsep}{4pt}\n\\caption{Comparison of benchmark and fine-tuned YOLO26s variants. $\\star$ = final selected model.}\n\\label{tab:finetune}\n\\begin{tabularx}{\\linewidth}{P{2.7cm} C C C C C C C}\n\\hline\n\\textbf{Model variant} & \\textbf{Val mAP50} & \\textbf{Val \\mbox{mAP50-95}} & \\textbf{Test Precision} & \\textbf{Test Recall} & \\textbf{Test mAP50} & \\textbf{Test \\mbox{mAP50-95}} & \\textbf{Infer. (ms)} \\\\\n\\hline\nBenchmark YOLO26s (640 px)          & 0.956 & 0.847 & 0.891 & 0.887 & 0.944 & 0.823 & 9.7 \\\\\nFine-tuned YOLO26s (640 px)         & 0.960 & 0.866 & 0.909 & 0.886 & 0.952 & 0.847 & 9.7 \\\\\nFine-tuned YOLO26s (960 px) $\\star$ & 0.971 & 0.895 & 0.909 & 0.904 & 0.962 & 0.876 & 19.6 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nThe 960-pixel fine-tuned model achieves a test mAP50-95 of 0.876, representing a gain of 5.3 percentage points over the benchmark YOLO26s and 8.1 points over the source-paper baseline architecture (YOLOv8s, 0.795). The three contributing steps are approximately equal in magnitude, as summarised in Table~\\ref{tab:gain}.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Decomposition of the accuracy gain from the source-paper baseline to the final model. pp = percentage points.}\n\\label{tab:gain}\n\\begin{tabularx}{\\linewidth}{P{4.0cm} P{4.0cm} C C C}\n\\hline\n\\textbf{Step} & \\textbf{Model / configuration} & \\textbf{Test mAP50} & \\textbf{Test mAP50-95} & \\textbf{Gain (pp \\mbox{mAP50-95})} \\\\\n\\hline\nBaseline (source paper arch.) & YOLOv8s, 60 ep, 640 px    & 0.916 & 0.795 & --- \\\\\nStep 1: Newer architecture    & YOLO26s, 60 ep, 640 px    & 0.944 & 0.823 & +2.8 \\\\\nStep 2: Extended training     & YOLO26s, +100 ep, 640 px  & 0.952 & 0.847 & +2.4 \\\\\nStep 3: Higher resolution     & YOLO26s, +100 ep, 960 px  & 0.962 & 0.876 & +2.9 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nFigure~\\ref{fig:curves} shows the precision--confidence, recall--confidence, F1--confidence and precision--recall curves of the final model on the validation set. The all-class F1 score peaks at 0.93 at a confidence of 0.551, and the precision--recall curve gives a validation mAP50 of 0.971, with per-class AP50 ranging from 0.936 (PET) to 0.981 (PS).\n\n\\begin{figure}[h!]\n\\centering\n\\begin{minipage}[t]{0.49\\textwidth}\n\\textbf{(A)}\\par\\vspace{2pt}\n\\includegraphics[width=\\linewidth]{BoxP_curve.png}\n\\end{minipage}\\hfill\n\\begin{minipage}[t]{0.49\\textwidth}\n\\textbf{(B)}\\par\\vspace{2pt}\n\\includegraphics[width=\\linewidth]{BoxR_curve.png}\n\\end{minipage}\\par\\vspace{8pt}\n\\begin{minipage}[t]{0.49\\textwidth}\n\\textbf{(C)}\\par\\vspace{2pt}\n\\includegraphics[width=\\linewidth]{BoxF1_curve.png}\n\\end{minipage}\\hfill\n\\begin{minipage}[t]{0.49\\textwidth}\n\\textbf{(D)}\\par\\vspace{2pt}\n\\includegraphics[width=\\linewidth]{BoxPR_curve.png}\n\\end{minipage}\n\\caption{Validation-set performance curves of the final model (YOLO26s fine-tuned at 960~px) for each polymer class and for all classes combined (thick blue line). \\textbf{(A)} Precision versus confidence threshold. \\textbf{(B)} Recall versus confidence threshold. \\textbf{(C)} F1 score versus confidence threshold; the all-class F1 score peaks at 0.93 at a confidence of 0.551. \\textbf{(D)} Precision--recall curve with per-class AP50 (ABS 0.979, Nylon 0.977, PE 0.976, PET 0.936, PS 0.981, PVC 0.976) and an all-class mAP50 of 0.971.}\\label{fig:curves}\n\\end{figure}\n\n\\FloatBarrier\n\\subsection{Final Model Error Analysis}\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Final model (YOLO26s, fine-tuned at 960 px) error analysis at three confidence thresholds on 234 test images.}\n\\label{tab:final_error}\n\\begin{tabularx}{\\linewidth}{C C C C C C}\n\\hline\n\\textbf{Confidence threshold} & \\textbf{Located (\\%)} & \\textbf{Missed} & \\textbf{Extra boxes} & \\textbf{Count bias/img} & \\textbf{Count MAE/img} \\\\\n\\hline\n0.25 & 96.0\\% & 136 & 620 & +2.07 & 2.43 \\\\\n0.40 & 94.2\\% & 196 & 425 & +0.98 & 1.72 \\\\\n0.50 & 92.9\\% & 241 & 328 & +0.37 & 1.46 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nThe class confusion matrix of the final model (Table~\\ref{tab:confusion}) reveals that polymer classification among located particles is effectively solved: the only residual misclassification is 17 PVC particles predicted as ABS (2.1\\% of located PVC particles). Every other located particle receives the correct polymer class.\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Class confusion matrix for the final model at confidence $\\geq$ 0.25. Rows = true polymer; columns = predicted polymer. Only located (matched) particles are counted. The sole confusion is 17 PVC particles predicted as ABS.}\n\\label{tab:confusion}\n\\begin{tabularx}{\\linewidth}{l C C C C C C}\n\\hline\n\\textbf{True $\\backslash$ Predicted} & \\textbf{ABS} & \\textbf{Nylon} & \\textbf{PE} & \\textbf{PET} & \\textbf{PS} & \\textbf{PVC} \\\\\n\\hline\nABS   & 322 & --- & ---   & --- & --- & --- \\\\\nNylon & --- & 643 & ---   & --- & --- & --- \\\\\nPE    & --- & --- & 1,302 & --- & --- & --- \\\\\nPET   & --- & --- & ---   & 60  & --- & --- \\\\\nPS    & --- & --- & ---   & --- & 150 & --- \\\\\nPVC   & 17  & --- & ---   & --- & --- & 739 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\nFigure~\\ref{fig:confusion_norm} shows the normalised confusion matrix computed by the Ultralytics validator on the validation set. Diagonal values range from 0.92 (PVC) to 0.99 (PE). The largest cross-polymer confusions involve PVC: 4\\% of PVC particles are predicted as ABS and 4\\% as Nylon, and 5\\% of ABS particles are predicted as PVC. The background column shows that detections matching no labelled particle are most often assigned to PE (33\\%), followed by Nylon and PVC (21\\% each).\n\n\\begin{figure}[h!]\n\\begin{center}\n\\includegraphics[width=0.75\\textwidth]{confusion_matrix_normalized.png}\n\\end{center}\n\\caption{Normalised confusion matrix of the final model on the validation set, computed by the Ultralytics validator. Columns give the true polymer class and rows the predicted class; each column is normalised to sum to one. The background column gives the predicted class of detections that match no labelled particle (false positives).}\\label{fig:confusion_norm}\n\\end{figure}\n\nFigure~\\ref{fig:val_examples} compares the ground-truth annotations with the final model's predictions for the first three validation batches.\n\n\\begin{figure}[h!]\n\\centering\n\\begin{minipage}[t]{2.2em}\\mbox{}\\end{minipage}%\n\\begin{minipage}[t]{0.8\\textwidth}\n\\makebox[0.49\\linewidth]{\\textbf{Ground truth}}\\hfill\\makebox[0.49\\linewidth]{\\textbf{Prediction}}\n\\end{minipage}\\par\\vspace{3pt}\n\\begin{minipage}[t]{2.2em}\\vspace{0pt}\\textbf{(A)}\\end{minipage}%\n\\begin{minipage}[t]{0.8\\textwidth}\\vspace{0pt}\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch0_labels.jpg}\\hfill\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch0_pred.jpg}\n\\end{minipage}\\par\\vspace{6pt}\n\\begin{minipage}[t]{2.2em}\\vspace{0pt}\\textbf{(B)}\\end{minipage}%\n\\begin{minipage}[t]{0.8\\textwidth}\\vspace{0pt}\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch1_labels.jpg}\\hfill\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch1_pred.jpg}\n\\end{minipage}\\par\\vspace{6pt}\n\\begin{minipage}[t]{2.2em}\\vspace{0pt}\\textbf{(C)}\\end{minipage}%\n\\begin{minipage}[t]{0.8\\textwidth}\\vspace{0pt}\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch2_labels.jpg}\\hfill\n\\includegraphics[width=0.49\\linewidth,trim=0 0 355bp 0,clip]{val_batch2_pred.jpg}\n\\end{minipage}\n\\caption{Ground-truth annotations (left) and predictions of the final model (right) for the first three validation batches (12 images each). Boxes are coloured by polymer class (Nylon, cyan; ABS, dark blue), and each predicted box is labelled with its confidence score. \\textbf{(A)} Batch 0: 12 Nylon images. \\textbf{(B)} Batch 1: nine Nylon and three ABS images. \\textbf{(C)} Batch 2: 12 ABS images.}\\label{fig:val_examples}\n\\end{figure}\n\n\\FloatBarrier\n\\subsection{Per-Polymer Improvement from Benchmark to Final Model}\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Per-polymer AP improvement from the benchmark YOLO26s to the final fine-tuned model. Classes with the most room for improvement (ABS, PE, PS, PVC) benefited most from higher-resolution fine-tuning.}\n\\label{tab:per_polymer_gain}\n\\begin{tabularx}{\\linewidth}{l C C C C C}\n\\hline\n\\textbf{Polymer} & \\textbf{Benchmark AP50} & \\textbf{Final AP50} & \\textbf{Benchmark \\mbox{AP50-95}} & \\textbf{Final \\mbox{AP50-95}} & \\textbf{\\mbox{AP50-95} gain (pp)} \\\\\n\\hline\nABS   & 0.900 & 0.922 & 0.753 & 0.825 & +7.2 \\\\\nNylon & 0.977 & 0.981 & 0.883 & 0.908 & +2.5 \\\\\nPE    & 0.954 & 0.962 & 0.795 & 0.865 & +7.0 \\\\\nPET   & 0.947 & 0.961 & 0.881 & 0.891 & +1.0 \\\\\nPS    & 0.951 & 0.977 & 0.813 & 0.887 & +7.4 \\\\\nPVC   & 0.936 & 0.970 & 0.814 & 0.883 & +6.9 \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\\section{Discussion}\n\\label{sec:discussion}\n\n\\subsection{Architectural Determinants of Detection Accuracy}\n\nThe benchmark reveals a significant, repeatable improvement in accuracy of around 2.7--3.3 mAP50-95 points when transitioning from YOLOv8 to the second-generation YOLO architectures (YOLO11, YOLO26, YOLOv10) on NR microplastic fluorescence images. This gain is seen in both validation and test set and is present in all six polymer classes, suggesting that this is not specific to a particular split of data, but is a genuine generalisation improvement.\n\nAmong the three best models, the two main architectural improvements that could be responsible for this improvement are the inclusion of a lightweight depthwise-separable classification branch (Y, YOLO11, and YOLO26) and self-attention on the coarsest feature map (Y, YOLO11, and C2PSA in YOLO26; PSA in YOLOv10). Self-attention can let the detector ``see'' the particle's context, across the whole coarsest-scale feature map (20$\\times$20 cells with 640-pixel input), which is potentially helpful for particles in aggregates whose background fluorescence intensity is affected by neighbouring particles. The lightweight classification branch helps to decrease overfitting in the class-prediction sub-network, which is important for two classes (PET and PS) with limited training examples.\n\nThe error analysis shows a slight reduction in the number of spurious detections for NMS-free dual-assignment training (YOLO26s, YOLOv10s) compared to NMS-post-processing architectures (YOLO11s, YOLOv8s, YOLOv9s) --- 620--829 extra boxes vs.\\ 890--1136. The main advantage of deployment with NMS-free inference is pipeline simplicity and not detection accuracy.\n\n\\subsection{Impact of Training Duration}\n\nIt is worth noting that convergence of all the benchmark models is not obtained at epoch 60. All the architectures have been showing improvement in the validation mAP50-95 over the last decade of training, and there are no obvious signs of performance plateauing. I think there are two possible explanations: (1) the dataset (1086 training images) is too small for fast convergence; (2) the learning-rate schedule (linear decay to 1\\% in 60 epochs) is too aggressive for the extent of fine-tuning of the COCO pretrained weights.\n\nThe fine-tuning campaign shows that 100 extra epochs of training, from the epoch-60 benchmark checkpoint using a new cosine learning-rate schedule, provide 2.4 mAP50-95 points at 640-pixel resolution. This is a greater improvement than many recent architectural advances in the YOLO family, and highlights the need for training schedule design in constrained-data regimes.\n\n\\subsection{Impact of Input Resolution}\n\nThe single biggest increase measured in this study is a 2.9 mAP50-95 increase from 640 to 960 pixels of inference resolution. This result is consistent with the particle size distribution, which show a median particle size of about 20$\\times$21 pixels at 640-pixel input and a lower limit of 10 pixels in the P3 feature scale. The same median particle at P3 has an input size of 30$\\times$32 pixels, and the minimum particle size that can be detected is reduced in the same proportion at 960-pixel input.\n\nThere is a price to the resolution gain: inference latency is doubled from 9.7~ms to 19.6~ms per image. The 640-pixel fine-tuned variant (mAP50-95 = 0.847) might be more desirable than the 960-pixel final model (0.876) for deployments where real-time or near real-time analysis is needed on a consumer GPU.\n\n\\subsection{The Counting Problem}\n\nThe problem of accurate particle counting is different from the problem of maximizing mAP, and is more challenging. To assess the mAP metric, the recall-precision tradeoff is optimized per IoU level, with the operator then having to choose a single threshold; in practice, the operator must choose the threshold. Table~\\ref{tab:final_error} shows the basic trade-off between choosing the threshold: a threshold of 0.25 gives maximum recall of 96.0\\% but has a positive count bias of +2.07 particles per image from spurious detections, while a threshold of 0.50 reduces the bias to +0.37 particles per image (an effective 97.5\\% accuracy assuming a mean image count of 14.6 particles) but has a recall of only 92.9\\%.\n\nThe few remaining spurious detections, at threshold 0.50, are concentrated in the PE images (highest particle density and highest intraclass morphological variability). Qualitative inspection shows that many of the additional boxes are on dim particles that were not annotated, if this is true, then the actual false positive rate is lower than the one reported and the actual deployment accuracy is higher than the mAP reported.\n\n\\FloatBarrier\n\\section{Conclusion}\n\\label{sec:conclusion}\n\nThis study presents a comprehensive evaluation of five YOLO-family object detectors for automated detection and polymer classification of Nile Red-stained microplastic particles in fluorescence microscopy images. The work makes five concrete contributions to the state of the art.\n\nFirst, a systematic data quality audit of the public \\citet{rermborirak2025} dataset uncovered a large-scale duplication artefact---1,012 redundant images representing 39.4\\% of the published corpus---accompanied by 180$^{\\circ}$ label-rotation errors in the duplicated copies. Removing this artefact is essential for valid model training and unbiased evaluation, and the cleaning procedure is fully automated and reproducible.\n\nSecond, a controlled benchmark across five YOLO architectures demonstrates that YOLO26s, YOLO11s, and YOLOv10s are statistically equivalent (test mAP50-95: 0.822--0.828) and collectively superior to YOLOv8s (0.795) by approximately 3 percentage points, confirming that recent architectural advances---particularly self-attention on the coarsest feature map and lightweight classification branches---transfer effectively to NR fluorescence microplastic images.\n\nThird, the fine-tuning campaign demonstrates that the benchmark accuracy is a lower bound: extending training by 100 epochs from the benchmark checkpoint adds approximately 2.4 mAP50-95 points at 640-pixel resolution, and increasing input resolution from 640 to 960 pixels adds a further 2.9 points, for a combined gain of 8.1 percentage points over the YOLOv8s source-paper baseline.\n\nFourth, the independent error analysis reveals that polymer classification of located particles is effectively solved---only 0.5\\% of located particles receive an incorrect polymer assignment---while the principal residual challenge is over-detection, primarily in high-density PE images where many dim, unlabelled particles appear to be genuine detections not captured in the ground-truth annotations.\n\nFifth, the final model (YOLO26s fine-tuned at 960-pixel resolution) achieves test precision 0.909, recall 0.904, mAP50 0.962, and mAP50-95 0.876. At a recommended operating threshold of 0.50, it counts particles with a mean absolute error of 1.46 per image and a bias of +0.37, corresponding to a relative accuracy of 97.5\\% on images averaging 14.6 labelled particles. The complete model, code, and experimental provenance are released to enable reproduction and downstream application in environmental monitoring workflows.\n\n\\FloatBarrier\n\\section*{Appendix A: Model Card for the Final Model}\n\\label{sec:appendixA}\n\n\\setcounter{table}{0}\n\\renewcommand{\\thetable}{A\\arabic{table}}\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\caption{Model card for the final YOLO26s fine-tuned model.}\n\\label{tab:model_card}\n\\begin{tabularx}{\\linewidth}{P{4.8cm} L}\n\\hline\n\\textbf{Attribute} & \\textbf{Value} \\\\\n\\hline\nArchitecture & YOLO26s (Ultralytics), end-to-end, NMS-free \\\\\nParameter count & 9,952,508 ($\\sim$10.0 M) \\\\\nComputational cost & 51.9 GFLOPs at 960-pixel input \\\\\nWeights file size & 20.4 MB \\\\\nInput specification & RGB image, letterboxed to 960 $\\times$ 960 pixels \\\\\nOutput specification & Bounding box (xyxy), polymer class (6 classes), confidence score per particle \\\\\nClasses & ABS, Nylon, PE, PET, PS, PVC \\\\\nTraining data & 1,086 images, 16,791 labelled particles \\\\\nTraining history & COCO-pretrained $\\rightarrow$ 60 epochs at 640 px $\\rightarrow$ 100 epochs at 960 px (cosine decay) \\\\\nTest precision & 0.909 \\\\\nTest recall & 0.904 \\\\\nTest mAP50 & 0.962 \\\\\nTest mAP50-95 & 0.876 \\\\\nCounting MAE ($\\tau = 0.50$) & 1.46 particles/image (mean 14.6 labelled particles/image) \\\\\nInference speed & 19.6 ms/image (NVIDIA RTX 3050, batch size 1) \\\\\nRecommended threshold (max recall) & 0.25 --- locates 96.0\\% of particles \\\\\nRecommended threshold (min count error) & 0.50 --- MAE 1.46, bias +0.37 particles/image \\\\\nIntended application & Research screening of NR-stained samples, single-polymer samples, same imaging protocol as training data \\\\\nKnown limitations & Not validated for mixed-polymer samples, other cameras, or polymers outside the six classes \\\\\nDataset licence & CC BY-NC-ND 4.0 (non-commercial use only; attribution required) \\\\\nSoftware licence & AGPL-3.0 (Ultralytics) \\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\n\\FloatBarrier\n\n\n\\bibliographystyle{Frontiers-Harvard} %  Many Frontiers journals use the Harvard referencing system (Author-date), to find the style and resources for the journal you are submitting to: https://zendesk.frontiersin.org/hc/en-us/articles/360017860337-Frontiers-Reference-Styles-by-Journal. For Humanities and Social Sciences articles please include page numbers in the in-text citations \n%\\bibliographystyle{Frontiers-Vancouver} % Many Frontiers journals use the numbered referencing system, to find the style and resources for the journal you are submitting to: https://zendesk.frontiersin.org/hc/en-us/articles/360017860337-Frontiers-Reference-Styles-by-Journal\n\\bibliography{test}\n\n%%% Make sure to upload the bib file along with the tex file and PDF\n%%% Please see the test.bib file for some examples of references\n\n%%% Figures are placed in the main text next to where they are first cited (Figures 1--3).\n%%% Remember to also upload the figure files when submitting your article.\n%%% Please be aware that for original research articles we only permit a combined number of 15 figures and tables, one figure with multiple subfigures will count as only one figure.\n%%% If you don't add the figures in the LaTeX files, please upload them when submitting the article.\n%%% Frontiers will add the figures at the end of the provisional pdf automatically\n%%% The use of LaTeX coding to draw Diagrams/Figures/Structures should be avoided. They should be external callouts including graphics.\n\n\\end{document}",
      "tex_filename": "frontiers.tex",
      "bib_content": "@article{article2026,\n  title={mnnnnn b},\n  author={Frontiers Authors},\n  journal={Frontiers in Education},\n  doi={10.3389/feduc.2026.8255139},\n  year={2026}\n}\n",
      "source_dir": "/journals/education/articles/10.3320/feduc.2026.82975539/source",
      "tex_file": "/journals/education/articles/10.3320/feduc.2026.82975539/source/article.tex",
      "bib_file": "/journals/education/articles/10.3320/feduc.2026.82975539/source/references.bib",
      "id": "art_8255139",
      "updated_at": "2026-11-07T11:56:37Z",
      "created_at": "2026-11-07T11:56:37Z"
    },
    {
      "title": "ConvNeXt\u2013KAN: A Kolmogorov\u2013Arnold Network Head for Robust Multi-class Staging of Alzheimer's Disease from Brain MRI",
      "authors": [
        {
          "name": "Kamrul Islam",
          "affiliations": [
            "1"
          ],
          "is_corresponding": true,
          "affil_str": "1,*",
          "initials": "KI"
        },
        {
          "name": "Belayet Hossen",
          "affiliations": [
            "2"
          ],
          "is_corresponding": false,
          "affil_str": "2",
          "initials": "BH"
        },
        {
          "name": "Md Takbir Alam Manjar",
          "affiliations": [
            "3"
          ],
          "is_corresponding": false,
          "affil_str": "3",
          "initials": "MM"
        },
        {
          "name": "Sharmin Sultana",
          "affiliations": [
            "4"
          ],
          "is_corresponding": false,
          "affil_str": "4",
          "initials": "SS"
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Gabelli School of Business, Fordham University, New York, United States"
        },
        {
          "index": "2",
          "text": "Master of Science in Information System Management Stanton University"
        },
        {
          "index": "3",
          "text": "Master of Science in Information System Stanton University"
        },
        {
          "index": "4",
          "text": "College of Science & Mathematics, Rowan University, Glassboro, New Jersey, United States"
        }
      ],
      "corr_author": "Kamrul Islam",
      "corr_email": "",
      "abstract": "Alzheimer's disease (AD) is a progressive neurodegenerative disorder for which accurate, stage-wise classification from structural magnetic resonance imaging (MRI) can support earlier intervention. Convolutional neural networks (CNNs) dominate this task, but the classifier heads they use rely on fixed activation functions and linear weights, which constrains the modeling of the subtle, highly non-linear atrophy and texture patterns that separate dementia stages. In addition, the widely used Open Access Series of Imaging Studies (OASIS) collection is severely imbalanced, and two common practices\u2014undersampling every class to the smallest one, and splitting at the image (slice) level\u2014 respectively discard most of the data and inflate reported accuracy. We address these issues with ConvNeXt\u2013KAN, a hybrid model that couples a transfer-learned ConvNeXt feature extractor with a Kolmogorov\u2013Arnold Network (KAN) classification head whose edges are learnable spline activations implemented efficiently with Gaussian radial basis functions. The model is trained with a robustness-oriented recipe (MixUp and CutMix, label smoothing, decoupled weight decay, a cosine learning-rate schedule with warm-up, and test-time augmentation) and a data strategy that uses far more of the imbalanced dataset while evaluating on a fixed, balanced, leakage-controlled test set. On the held-out test set the model attains 94.5% accuracy, a macro-averaged F1 of 0.944, and a mean one-vs-rest ROC\u2013AUC of 0.991, with an ablation confirming that pretrained features and expanded data are the main drivers of performance. The learnable-activation head improves discrimination of the difficult non-demented versus very-mild-demented boundary, and the efficient formulation keeps the approach practical in standard deep-learning frameworks. To assess out-of-distribution robustness we further evaluate the trained model, without any fine-tuning, on an independent four-class Alzheimer's MRI collection distributed on Kaggle; test-time-augmented accuracy is 61.6% with a macro-averaged F1 of 0.565, and a class-wise analysis shows that moderate dementia continues to be recognized perfectly while the two clinically intermediate stages absorb most of the domain-shift error. We further quantify the impact of evaluation protocol and argue that subject-level validation is essential before clinical claims.",
      "keywords": "Alzheimer's disease, brain MRI, Kolmogorov\u2013Arnold network, ConvNeXt, transfer learning, deep learning, medical image classification, class imbalance",
      "doi": "10.3389/fsoc.2026.2804691",
      "article_url_path": "/journals/sociology/articles/10.3389/fsoc.2026.2804691/abstract",
      "journal_slug": "sociology",
      "journal": "Frontiers in Sociology",
      "journal_abbrev": "Front. Sociol.",
      "section": "Sec. Sociology of Law",
      "banner": "/assets/images/journals/sociology-banner.png",
      "issn": "2297-7775",
      "impact_factor": "2.3",
      "citescore": "4",
      "received": "2026-10-20",
      "accepted": "2026-11-01",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
      "views_count": "10",
      "demographics": [
        {
          "name": "United States",
          "views": 6
        },
        {
          "name": "India",
          "views": 4
        }
      ],
      "id": "art_2804599",
      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Frontiers manuscript -- ConvNeXt-KAN for Alzheimer's MRI staging\n% Compile with the Frontiers LaTeX package (FrontiersinHarvard.cls + Frontiers-Harvard.bst).\n% Upload this .tex, test.bib, and the figure files (see \"Figure captions\" at the end).\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass[utf8]{FrontiersinHarvard} % Harvard Referencing Style (Author-Date)\n\n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\\usepackage{amsmath,amssymb}\n\\usepackage{booktabs}\n\n\\linenumbers\n\n% Leave a blank line between paragraphs instead of using \\\\\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\\def\\firstAuthorLast{Islam {et~al.}}\n\\def\\Authors{Kamrul Islam\\,$^{1,*}$, Belayet Hossen\\,$^{2}$, Md Takbir Alam Manjar\\,$^{3}$ and Sharmin Sultana\\,$^{4}$}\n\\def\\Address{$^{1}$Gabelli School of Business, Fordham University, New York, United States \\\\\n$^{2}$Master of Science in Information System Management\nStanton University \\\\\n$^{3}$Master of Science in Information System\nStanton University  \\\\\n$^{4}$College of Science \\& Mathematics, Rowan University, Glassboro, New Jersey, United States}\n\\def\\corrAuthor{Kamrul Islam}\n\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title[ConvNeXt--KAN for Alzheimer's MRI Staging]{ConvNeXt--KAN: A Kolmogorov--Arnold Network Head for Robust Multi-class Staging of Alzheimer's Disease from Brain MRI}\n\n\\author[\\firstAuthorLast ]{\\Authors} % This field will be automatically populated\n\\address{} % This field will be automatically populated\n\\correspondance{} % This field will be automatically populated\n\n\\extraAuth{}\n\n\\maketitle\n\n\\begin{abstract}\n\\section{}\nAlzheimer's disease (AD) is a progressive neurodegenerative disorder for which accurate, stage-wise\nclassification from structural magnetic resonance imaging (MRI) can support earlier intervention.\nConvolutional neural networks (CNNs) dominate this task, but the classifier heads they use rely on\nfixed activation functions and linear weights, which constrains the modeling of the subtle, highly\nnon-linear atrophy and texture patterns that separate dementia stages. In addition, the widely used\nOpen Access Series of Imaging Studies (OASIS) collection is severely imbalanced, and two common\npractices---undersampling every class to the smallest one, and splitting at the image (slice) level---\nrespectively discard most of the data and inflate reported accuracy. We address these issues with\n\\emph{ConvNeXt--KAN}, a hybrid model that couples a transfer-learned ConvNeXt feature extractor with a\n\\emph{Kolmogorov--Arnold Network} (KAN) classification head whose edges are learnable spline\nactivations implemented efficiently with Gaussian radial basis functions. The model is trained with a\nrobustness-oriented recipe (MixUp and CutMix, label smoothing, decoupled weight decay, a cosine\nlearning-rate schedule with warm-up, and test-time augmentation) and a data strategy that uses far more\nof the imbalanced dataset while evaluating on a fixed, balanced, leakage-controlled test set. On the\nheld-out test set the model attains 94.5\\% accuracy, a macro-averaged F1 of 0.944, and a mean one-vs-rest\nROC--AUC of 0.991, with an ablation confirming that pretrained features and expanded data are the main\ndrivers of performance. The learnable-activation head improves discrimination of the difficult\nnon-demented versus very-mild-demented boundary, and the efficient formulation keeps the approach\npractical in standard deep-learning frameworks. To assess out-of-distribution robustness we further\nevaluate the trained model, without any fine-tuning, on an independent four-class Alzheimer's MRI\ncollection distributed on Kaggle; test-time-augmented accuracy is $61.6\\%$ with a macro-averaged F1 of\n$0.565$, and a class-wise analysis shows that moderate dementia continues to be recognized perfectly\nwhile the two clinically intermediate stages absorb most of the domain-shift error. We further quantify\nthe impact of evaluation protocol and argue that subject-level validation is essential before clinical\nclaims.\n\n\\tiny\n\\keyFont{ \\section{Keywords:} Alzheimer's disease, brain MRI, Kolmogorov--Arnold network, ConvNeXt, transfer learning, deep learning, medical image classification, class imbalance}\n\\end{abstract}\n\n\\section{Introduction}\n\nAlzheimer's disease (AD) is the leading cause of dementia, accounting for an estimated 60--70\\% of cases,\nand the number of people living with dementia worldwide is projected to rise sharply as populations age\n\\citep{alzassoc2023}. AD progresses along a clinical continuum---from cognitively normal, through very mild\nand mild cognitive decline, to moderate and severe dementia---and the greatest therapeutic benefit is\nobtained when intervention begins early, before irreversible neuronal loss \\citep{alzassoc2023}.\nConsequently, methods that not only separate diseased from healthy brains but also resolve the \\emph{stage}\nof impairment have direct clinical value for triage, longitudinal monitoring, and the selection of patients\nfor emerging disease-modifying therapies.\n\nStructural magnetic resonance imaging (MRI) is a central, non-invasive modality for characterizing AD,\nrevealing hippocampal atrophy, medial-temporal-lobe thinning, and ventricular enlargement that progress\nwith disease severity \\citep{marcus2007oasis}. However, the structural changes that distinguish the\n\\emph{earliest} stages are subtle, spatially distributed, and difficult to appreciate even for experienced\nreaders, contributing to inter-rater variability and a heavy reporting workload. Automated, learning-based\nanalysis therefore offers a route to reproducible, scalable, and stage-aware decision support that can\ncomplement expert assessment. Recent comparative studies confirm that machine learning and deep learning\napproaches consistently outperform classical statistical tests in distinguishing dementia stages from MRI\ndata \\citep{aslan2025jcma,aslan2025jastt,aslan2025int}.\n\nOver the past decade, deep learning has transformed medical image analysis \\citep{litjens2017survey}.\nConvolutional neural networks (CNNs)---from AlexNet \\citep{krizhevsky2012alexnet} and VGG\n\\citep{simonyan2015vgg} to residual \\citep{he2016resnet}, densely connected \\citep{huang2017densenet}, and\ncompound-scaled \\citep{tan2019efficientnet} architectures---learn hierarchical features directly from pixels\nand now dominate AD classification from MRI. Because labeled medical data are scarce relative to the\ncapacity of modern networks, these models are typically initialized with weights pretrained on large\nnatural-image corpora such as ImageNet \\citep{deng2009imagenet} and then fine-tuned on the target task; this\ntransfer-learning strategy consistently improves accuracy and training stability on small datasets\n\\citep{chui2022mri,pandey2024transfer,basheer2021dementia}.\n\nDespite strong reported results, three recurring issues limit the reliability and the headroom of current\npipelines. \\emph{First}, the classifier head placed on top of CNN features is almost always a multilayer\nperceptron (MLP) with \\emph{fixed} activation functions (e.g., ReLU or GELU \\citep{hendrycks2016gelu}) and\nlinear weights. Such networks exhibit a spectral bias toward low-frequency functions and may require many\nparameters to represent the fine, highly non-linear texture and atrophy gradients that separate adjacent\ndementia stages \\citep{liu2024kan,yang2025medkan}. \\emph{Second}, public AD datasets are severely\nimbalanced: in the OASIS collection studied here the moderate-dementia class contains only $488$ slices\nagainst $67{,}222$ non-demented slices---roughly two orders of magnitude fewer. A widespread remedy is to\nundersample every class down to the size of the smallest one, which discards the overwhelming majority of\nthe available data and starves precisely the under-represented and clinically difficult categories of\ntraining signal \\citep{shorten2019augmentation}. \\emph{Third}, many of the very high accuracies\n($\\geq 99\\%$) reported on these data are obtained with image-level (per-slice) train/test splitting. Because\neach three-dimensional scan contributes many adjacent two-dimensional slices, slice-level splitting can\nplace near-duplicate slices of the same patient in both the training and test partitions, leaking subject\nidentity and inflating measured performance relative to genuine, patient-independent generalization.\n\nA promising response to the first issue has recently emerged from outside computer vision.\n\\emph{Kolmogorov--Arnold Networks} (KANs), introduced by \\citet{liu2024kan} and grounded in the\nKolmogorov--Arnold representation theorem, replace the fixed activations and linear weights of an MLP with\n\\emph{learnable} univariate functions placed on the network's edges, classically parameterized by\nB-splines. KANs have demonstrated greater expressivity and interpretability than comparably sized MLPs and a\nreduced bias toward high-frequency components, and efficient reformulations such as FastKAN---which\napproximates the spline basis with Gaussian radial basis functions---make them practical at scale\n\\citep{li2024fastkan}. In medical imaging specifically, KAN-based models have been reported to capture\nintricate texture better than CNN- and Transformer-based baselines \\citep{yang2025medkan,bodner2024convkan}.\nMore recently, \\citet{manzari2025medvitv2} incorporated KAN layers into a medical Vision Transformer\n(MedViTV2) to achieve state-of-the-art robustness on 27 clean and corrupted medical imaging benchmarks,\nwhile reducing computational complexity by 44\\%; and \\citet{gao2025msfkan} proposed a multi-scale feature\nprediction network (MSFKAN) that fuses KAN modules across spatial scales, outperforming fully connected\nbaselines on several medical classification tasks.\nThese developments motivate a simple but, to our knowledge, under-explored design for AD staging: retain a\npowerful, transfer-learned convolutional backbone for feature extraction, but replace the conventional MLP\nclassifier with a KAN head whose learnable activations can model subtle, non-linear class boundaries.\n\nBuilding on this insight, we propose \\emph{ConvNeXt--KAN} and make the following contributions:\n\\begin{enumerate}\n\\item \\textbf{A ConvNeXt--KAN hybrid for AD staging.} We pair a transfer-learned ConvNeXt backbone with a\nKAN classification head, implemented efficiently via the radial-basis-function formulation of\n\\citet{li2024fastkan}. To our knowledge this is among the first uses of a learnable-activation KAN head for\nmulti-class Alzheimer's staging from MRI, and it improves modeling of the subtle non-linear patterns that\nfixed-activation heads handle poorly.\n\\item \\textbf{A robustness-oriented training recipe for small, imbalanced medical data} that combines\ntransfer learning with MixUp and CutMix, label smoothing, decoupled weight decay (AdamW), a cosine\nlearning-rate schedule with warm-up, and test-time augmentation.\n\\item \\textbf{A data-utilization and evaluation protocol} that uses far more of the imbalanced dataset by\ncapping abundant classes and oversampling only the training partition, while holding out a fixed, balanced,\nleakage-controlled test set. We additionally analyze subject-level leakage as a confound in prior reports.\n\\item \\textbf{An empirical study} in which ConvNeXt--KAN attains 94.5\\% accuracy, 0.944 macro-F1, and 0.991\nmean ROC--AUC on the balanced test set, together with an ablation isolating the contribution of pretrained\nfeatures and expanded data.\n\\item \\textbf{A backbone comparison} across ConvNeXt-Tiny, ConvNeXt-Base, EfficientNetB4, DenseNet121, and\nViT-B/16 that justifies the choice of Tiny as the most capacity-efficient option for this data regime\n(Section~\\ref{sec:backbone_comparison}).\n\\item \\textbf{A comparative novelty analysis} summarising how ConvNeXt--KAN differs from existing KAN-based\nmedical imaging studies along architecture, task, and evaluation dimensions\n(Section~\\ref{sec:novelty}).\n\\end{enumerate}\n\n\\section{Related Work}\n\n\\subsection{Deep learning for Alzheimer's classification from MRI}\nEarly automated AD assessment relied on handcrafted morphometric descriptors---regional volumes, cortical\nthickness, and hippocampal shape---fed to classical classifiers such as support vector machines and random\nforests \\citep{basheer2021dementia}. While interpretable, these pipelines depend on accurate prior\nsegmentation and on feature engineering that may miss diffuse, sub-regional changes. CNNs subsequently\nimproved accuracy by learning hierarchical representations end-to-end, and two broad families have emerged:\nthree-dimensional networks that operate on whole volumes and preserve inter-slice context, and\ntwo-dimensional networks that classify individual slices and benefit directly from ImageNet pretraining\n\\citep{deng2009imagenet}. Because curated three-dimensional datasets are small, transfer learning with\ntwo-dimensional backbones such as ResNet \\citep{he2016resnet}, DenseNet \\citep{huang2017densenet}, and\nEfficientNet \\citep{tan2019efficientnet} has become the dominant and most data-efficient strategy\n\\citep{chui2022mri,pandey2024transfer}. On the public Kaggle OASIS collection in particular, numerous\nstudies report accuracies approaching or exceeding $99\\%$, frequently using aggressive augmentation or\noversampling to counter class imbalance \\citep{shorten2019augmentation}. However, these figures are commonly\nobtained with image-level splitting, which complicates fair comparison and may overstate generalization to\nunseen patients; relatively few works explicitly control for subject-level leakage or report class-balanced\nmetrics, motivating the careful evaluation protocol adopted here. Very recent work has continued to push\naccuracy on this benchmark using Transformer-based architectures: \\citet{aslan2025jastt} report competitive\nresults with a MaxViT-based framework on the same Kaggle OASIS four-class data, while \\citet{aslan2025jcma}\noffer a systematic comparison of classical machine-learning and shallow-neural models evaluated through\ncross-validation, providing a useful lower-bound reference. \\citet{aslan2025int} further demonstrate the\nutility of deep learning for intelligent-systems-based AD staging across multiple classification\nprotocols, reinforcing the evidence that learned feature representations are consistently superior to\nhandcrafted descriptors on this benchmark. Brain-tumor segmentation architectures such as\nthe VGG19--U-Net hybrid of \\citet{aslan2026mrl} further illustrate the breadth of deep-learning methods\nbeing applied across MRI-based neuroimaging tasks.\n\n\\subsection{Modern visual backbones}\nThe backbone literature has evolved from the first deep CNNs \\citep{krizhevsky2012alexnet,simonyan2015vgg}\nthrough residual and densely connected designs \\citep{he2016resnet,huang2017densenet} that enabled very deep\ntraining, aided by normalization \\citep{ioffe2015batchnorm} and smooth activations \\citep{hendrycks2016gelu}.\nThe Transformer \\citep{vaswani2017attention} and its vision counterpart \\citep{dosovitskiy2021vit} then\nshowed that attention-based models can match or surpass CNNs given sufficient data. In response, ConvNeXt\n\\citep{liu2022convnext} modernized the pure convolutional design---adopting larger depthwise kernels,\ninverted bottlenecks, layer normalization, and GELU activations---to match Transformer accuracy while\nretaining the locality, translation equivariance, and efficiency that are advantageous when training data\nare limited; ConvNeXt~V2 further strengthened representations through masked-autoencoder pretraining\n\\citep{woo2023convnextv2}. These properties make ConvNeXt an attractive feature extractor for medical\nimaging, where strong transferable features and parameter efficiency are both important.\n\n\\subsection{Kolmogorov--Arnold Networks}\nKANs are grounded in the Kolmogorov--Arnold representation theorem, a resolution of Hilbert's thirteenth\nproblem, which states that any multivariate continuous function can be written as a finite composition of\ncontinuous univariate functions and additions \\citep{liu2024kan}. Building on this theorem,\n\\citet{liu2024kan} parameterize the univariate edge functions with B-splines, producing networks that are\noften more expressive and more interpretable than MLPs of comparable size, with weaker spectral bias.\nA practical drawback is computational cost: evaluating and rescaling B-spline bases (via De Boor's\nrecursion) is expensive, which has spurred a rapid succession of efficient variants. \\citet{li2024fastkan}\nprove that third-order B-splines can be closely approximated by Gaussian radial basis functions, giving\n\\emph{FastKAN}, a substantially faster and numerically more stable formulation that uses layer normalization\nto keep activations within the effective basis range. Convolutional KANs, which replace the linear maps in\nconvolutions with KAN edges, have been formalized by \\citet{bodner2024convkan}, and a growing body of work\nsurveys the design space \\citep{somvanshi2024kansurvey}. In medical image classification,\n\\citet{yang2025medkan} introduce MedKAN with local- and global-information KAN modules and report that\nKAN-based models capture fine texture detail better than CNN- and Transformer-based baselines across\nmultiple datasets. Our work is complementary and deliberately lightweight: rather than building a full\nKAN or convolutional-KAN backbone, we retain a pretrained ConvNeXt feature extractor and use a KAN only as\nthe \\emph{classification head}, combining transfer-learned representations with learnable-activation\ndecision boundaries at modest additional cost.\n\n\\subsection{Regularization, optimization, and training strategies}\nModern recipes for small-data training combine several complementary techniques. Dropout\n\\citep{srivastava2014dropout} and batch normalization \\citep{ioffe2015batchnorm} reduce co-adaptation and\nstabilize optimization, while data augmentation broadly improves generalization \\citep{shorten2019augmentation}.\nMixUp \\citep{zhang2018mixup} and CutMix \\citep{yun2019cutmix} extend augmentation to the label space by\nforming convex or patch-wise combinations of examples and their targets, implementing a form of vicinal\nrisk minimization that smooths decision boundaries and improves robustness to corruption and to label noise.\nLabel smoothing \\citep{szegedy2016rethinking} discourages overconfident predictions and improves\ncalibration. On the optimization side, adaptive methods such as Adam \\citep{kingma2015adam} accelerate\nconvergence, and AdamW \\citep{loshchilov2019adamw} decouples weight decay from the adaptive update, which\nimproves generalization relative to coupled $L_2$ regularization. Cosine learning-rate schedules with\nwarm-up are widely used to stabilize early training and anneal smoothly to good minima. At inference,\ntest-time augmentation aggregates predictions over multiple transformed views, acting as a lightweight\nensemble that reduces variance. We combine these elements into a single recipe tailored to the small,\nimbalanced AD-staging setting.\n\n\\subsection{Emerging architectures and explainability}\nBeyond attention- and convolution-based designs, state-space models such as Mamba \\citep{gu2023mamba} and\nits bidirectional vision variant \\citep{zhu2024visionmamba} offer linear-time sequence modeling and are an\nactive direction for efficient image backbones; we regard them as complementary alternatives for future\nstudy. Orthogonally, clinical deployment requires not only accuracy but also trust: gradient-based\nexplanation methods such as Grad-CAM \\citep{selvaraju2017gradcam} localize the image regions that drive a\nprediction and, together with probability calibration, are important for translating models such as ours\ninto practice. We return to these directions in the conclusion.\n\n\\subsection{Research gap}\nIn summary, prior work has separately advanced (i) transfer learning with strong CNN backbones for AD\nclassification, (ii) KANs as a more expressive alternative to MLPs, and (iii) modern regularization. To our\nknowledge, however, no existing study combines a pretrained modern backbone with a learnable-activation KAN\nhead for \\emph{multi-class} Alzheimer's staging, while simultaneously addressing the severe class imbalance\nof OASIS through high data utilization and reporting performance under a balanced, leakage-controlled\nprotocol. ConvNeXt--KAN is designed to fill this gap.\n\n\\section{Materials and Methods}\n\n\\subsection{Overview}\nThe proposed pipeline has four stages: (i) an imbalance-aware, leakage-controlled construction of the\ntraining, validation, and test sets; (ii) on-the-fly augmentation with MixUp and CutMix; (iii) a model that\nextracts features with a transfer-learned ConvNeXt backbone and classifies them with a Kolmogorov--Arnold\nNetwork (KAN) head; and (iv) a two-phase optimization schedule followed by test-time augmentation at\ninference. The guiding design principle is to maximize the information drawn from a small, severely\nimbalanced dataset while keeping the evaluation faithful to patient-independent generalization, and to give\nthe classifier the capacity to model non-linear class boundaries without inflating the parameter count of\nthe backbone. Each component is described and justified below. The end-to-end pipeline is summarized in\nFigure~\\ref{fig:framework}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{1.png}\n\\caption{Overview of the proposed ConvNeXt--KAN framework for multi-class Alzheimer's disease staging.\nOASIS axial MRI slices are RGB-replicated and resized to $224\\times 224$, augmented with random flip,\nrotation, zoom, contrast jitter, MixUp and CutMix (Section~3.4), passed through the ImageNet-pretrained\nConvNeXt-Tiny backbone (four stages) and global average pooling to a 768-dimensional feature vector, and\nmapped to the four Alzheimer's stages (non-demented, very mild, mild, moderate) by a two-layer KAN head\n($768\\!\\to\\!128\\!\\to\\!4$) with dropout and softmax.}\n\\label{fig:framework}\n\\end{figure}\n\n\\subsection{Dataset and preprocessing}\nWe use the cross-sectional OASIS MRI collection \\citep{marcus2007oasis} in its publicly distributed\nfour-class form, comprising $86{,}437$ axial slices labeled as non-demented ($67{,}222$), very mild\ndementia ($13{,}725$), mild dementia ($5{,}002$), and moderate dementia ($488$); these four labels\ncorrespond to successive stages of the AD clinical continuum, so the task is an ordinal-flavored multi-class\nproblem in which adjacent classes are visually most similar.\n\n\\textbf{MRI slice selection and quality control.}\nThe OASIS dataset as distributed on Kaggle provides pre-extracted axial slices spanning the full\nbrain volume of each participant. We retain all available axial slices without restricting to a\nspecific anatomical range (e.g., hippocampal level), because the class labels are attached to the\nscan level rather than to individual slices and because restricting to a narrow slice range would\nartificially discard the majority of the available data for the already under-represented minority\nclasses. Each image file is verified for readability (non-zero byte count and successful decoding),\nand any corrupt or unreadable files are excluded. To address the potential for near-duplicate\nimages\u2014which arise because a single three-dimensional scan contributes many adjacent two-dimensional\nslices\u2014our sampling protocol caps each class at $T=1{,}500$ slices (Section~\\ref{subsec:split})\nand applies the train/test split \\emph{before} any oversampling, so that the test set is always\ndrawn from the raw, unaugmented pool. Because the publicly distributed OASIS slice collection does\nnot include per-slice subject identifiers, we are unable to perform an exact pixel-level\ndeduplication or a strict subject-level split; we explicitly acknowledge this as a remaining\nlimitation in Section~\\ref{sec:discussion_limits} and identify subject-level partitioning as the\nmost important direction for future work. For completeness, no images were found to be exact\nbit-for-bit duplicates across partition boundaries under our split procedure, though near-duplicate\nslices from the same subject may still appear in different partitions due to the lack of subject\ngrouping information.\n\n\\textbf{Image preprocessing.}\nEach image is decoded to three channels, with single-channel scans replicated across the channel\ndimension so that no images are silently discarded; this also matches the three-channel input\nexpected by ImageNet-pretrained filters and lets the backbone reuse its learned color/intensity\nkernels. Images are resized to $224\\times224$ pixels to match ConvNeXt's native training resolution,\nwhich preserves the validity of the pretrained receptive fields, and pixel values are left in the\n$[0,255]$ range because the ConvNeXt stem applies its own internal normalization; passing\npre-scaled inputs would double-normalize the data and degrade the features. Let\n$\\mathcal{D}=\\{(x_i,y_i)\\}_{i=1}^{N}$ denote the resulting image--label pairs with $C=4$ classes. The\nempirical class distribution and the visual heterogeneity of the four stages are illustrated in\nFigures~\\ref{fig:class_dist}--\\ref{fig:class_mean}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{Screenshot_44.png}\n\\caption{Original OASIS class distribution as a bar chart (left) and pie chart (right). The corpus is\nseverely imbalanced: $77.8\\%$ of slices are non-demented, $15.9\\%$ very mild, $5.8\\%$ mild, and only $0.6\\%$\nmoderate, motivating the imbalance-aware sampling protocol of Section~3.3.}\n\\label{fig:class_dist}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{Screenshot_45.png}\n\\caption{Representative axial MRI slices for three of the four OASIS classes (non-demented, mild dementia,\nmoderate dementia; five examples each). Adjacent stages differ subtly in cortical and ventricular\nmorphology, making the task ordinal-flavored: the visually most similar class pairs are also the clinically\nmost similar ones.}\n\\label{fig:mri_samples}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{Screenshot_46.png}\n\\caption{Mean image per class over the OASIS axial slices. The progression from non-demented to moderate\nshows a visible expansion of the ventricular regions and a thinning of cortical structure, consistent with\nthe expected anatomical correlates of disease progression.}\n\\label{fig:class_mean}\n\\end{figure}\n\n\\subsection{Imbalance-aware sampling and leakage-controlled split}\n\\label{subsec:split}\nThe extreme class imbalance admits two naive remedies, both flawed. Undersampling every class to the\nsmallest one (here $488$ images) yields a balanced set but discards roughly $98\\%$ of the data and starves\nthe difficult classes of training signal. Conversely, oversampling minority classes by duplication\n\\emph{before} splitting can place identical images in both the training and test sets, leaking information\nand inflating accuracy. We therefore adopt a three-part strategy that avoids both failure modes. First, we\ncap each class at $T$ images, which bounds computation and prevents the most frequent class from dominating.\nSecond, we hold out a fixed, \\emph{balanced} number of images per class for validation ($V$) and test\n($E$); a balanced test set makes per-class metrics directly comparable and renders the macro-averaged F1 a\nmeaningful summary, since each stage contributes equally regardless of its prevalence. Third, we balance\n\\emph{only} the training partition to the size of its largest class by random replication,\n\\begin{equation}\nN^{\\ast}=\\max_{c\\in\\{1,\\dots,C\\}} n_c, \\qquad a_c = N^{\\ast}-n_c,\n\\label{eq:oversample}\n\\end{equation}\nwhere $n_c$ is the number of training images of class $c$ after the held-out sets are removed and $a_c$ is\nthe number of additional (resampled) images added for that class. After balancing, each class is drawn with\nequal probability $1/C$ within a mini-batch, which equalizes the gradient contribution across stages.\nCrucially, because replication is applied \\emph{after} the split and only to training images, no validation\nor test image is ever duplicated into training, eliminating duplication leakage; and because the geometric\nand photometric augmentation below is sampled afresh each epoch, replicated images appear in different forms\nand are not merely memorized. The full protocol is summarized in Figure~\\ref{fig:imbalance_protocol}, and\nthe resulting balanced training and test partitions are shown in Figure~\\ref{fig:balanced_split}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{2.png}\n\\caption{Imbalance-aware data construction and leakage-control protocol. From the original imbalanced OASIS\ndistribution, each class is capped at $T=1{,}500$ slices; balanced validation and test sets are held out\n\\emph{before} any oversampling, eliminating train--test leakage; only the remaining training partition is\noversampled to the size of its largest class (Eq.~\\ref{eq:oversample}), producing the balanced training\ndistribution at the bottom.}\n\\label{fig:imbalance_protocol}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.85\\textwidth]{Screenshot_47.png}\n\\caption{Per-class sample counts after the imbalance-aware split. Training (left) is balanced by\noversampling, giving the same effective gradient contribution per stage; the held-out test set (right) is\nbalanced by construction at $E=73$ images per class, making macro-averaged metrics directly interpretable.}\n\\label{fig:balanced_split}\n\\end{figure}\n\n\\subsection{Data augmentation: MixUp and CutMix}\nOn top of mild geometric and photometric augmentation (horizontal flip, small rotation, zoom, translation,\nand contrast jitter), each training batch is regularized with MixUp or CutMix. The geometric ranges are kept\ndeliberately small and exclude vertical flips and large rotations, because such transforms would produce\nanatomically implausible brains and could harm rather than help learning; the chosen perturbations instead\nemulate realistic variation in head positioning and acquisition. MixUp \\citep{zhang2018mixup} forms convex\ncombinations of image pairs and their one-hot labels,\n\\begin{equation}\n\\tilde{x}=\\lambda x_i+(1-\\lambda)x_j, \\qquad\n\\tilde{y}=\\lambda y_i+(1-\\lambda)y_j, \\qquad\n\\lambda\\sim\\mathrm{Beta}(\\alpha,\\alpha),\n\\label{eq:mixup}\n\\end{equation}\nwhile CutMix \\citep{yun2019cutmix} pastes a rectangular patch from one image onto another and mixes labels in\nproportion to the patch area,\n\\begin{equation}\n\\tilde{x}=\\mathbf{M}\\odot x_i+(\\mathbf{1}-\\mathbf{M})\\odot x_j, \\qquad\n\\tilde{y}=\\lambda\\, y_i+(1-\\lambda)\\, y_j, \\qquad\n\\lambda = 1-\\frac{|\\mathcal{B}|}{WH},\n\\label{eq:cutmix}\n\\end{equation}\nwhere $\\mathbf{M}\\in\\{0,1\\}^{W\\times H}$ is the binary mask of the pasted box $\\mathcal{B}$, $\\odot$ is the\nHadamard product, and $W,H$ are the image width and height. Both schemes implement a form of vicinal risk\nminimization that smooths the decision boundary between adjacent stages and improves robustness; their\n\\emph{soft} targets also complement the label smoothing introduced below. One of the two schemes is selected\nat random per batch, and mixing is applied only during training (never to the held-out sets).\n\n\\subsection{Backbone}\nThe backbone is ConvNeXt-Tiny \\citep{liu2022convnext}, pretrained on ImageNet \\citep{deng2009imagenet} and\nused as a feature extractor with global average pooling. We choose the Tiny variant ($\\approx\\!28$M\nparameters) deliberately: larger backbones overfit readily on a training set of only a few thousand images,\nwhereas Tiny offers a favorable capacity--regularization trade-off while still providing the modern\ndesign elements (large depthwise kernels, inverted bottlenecks, layer normalization, GELU) that make\nConvNeXt competitive with Transformers. We confirm this choice empirically in\nSection~\\ref{sec:backbone_comparison}, where ConvNeXt-Tiny is benchmarked against ConvNeXt-Base,\nEfficientNetB4, DenseNet121, and ViT-B/16 under identical conditions. Global average pooling over the final feature map yields a compact,\npermutation-stable descriptor that maps an input image $x$ to a feature vector\n\\begin{equation}\n\\mathbf{z}=f_{\\theta}(x)\\in\\mathbb{R}^{d},\\qquad d=768 .\n\\label{eq:backbone}\n\\end{equation}\nDuring the first training phase the backbone parameters $\\theta$ are frozen so that the pretrained features\nare preserved while the head adapts (Section~\\ref{subsec:opt}). The internal stage structure of the\nConvNeXt-Tiny backbone used here is shown in Figure~\\ref{fig:convnext_backbone}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{3.png}\n\\caption{Internal architecture of the ConvNeXt-Tiny backbone. A $224\\times 224\\times 3$ input MRI passes\nthrough a $4\\times 4$ patchify stem (stride 4) to a $56\\times 56\\times 96$ feature map and through four\nstages of ConvNeXt blocks ($3{+}3{+}9{+}3$ blocks) with $2\\times 2$ stride-2 downsampling between stages.\nEach block applies a $7\\times 7$ depthwise convolution, LayerNorm, pointwise convolution, GELU, and a final\npointwise convolution with a residual connection (pre-norm design). Global average pooling on the final\n$7\\times 7\\times 768$ map yields the 768-dimensional feature vector $\\mathbf{z}$ of Eq.~\\ref{eq:backbone}.}\n\\label{fig:convnext_backbone}\n\\end{figure}\n\n\\subsection{Kolmogorov--Arnold Network head}\nThe classifier is a KAN, motivated by the Kolmogorov--Arnold representation theorem: for a continuous\n$f:[0,1]^{n}\\to\\mathbb{R}$ there exist continuous univariate functions $\\Phi_q$ and $\\phi_{q,p}$ such that\n\\begin{equation}\nf(x_1,\\dots,x_n)=\\sum_{q=1}^{2n+1}\\Phi_q\\!\\left(\\sum_{p=1}^{n}\\phi_{q,p}(x_p)\\right).\n\\label{eq:ka}\n\\end{equation}\nWhereas a conventional MLP head applies a \\emph{fixed} non-linearity after a linear map, a KAN layer places\na \\emph{learnable} univariate function on each edge and sums at the nodes. A layer mapping\n$\\mathbf{z}\\in\\mathbb{R}^{d_{\\mathrm{in}}}$ to $\\mathbf{u}\\in\\mathbb{R}^{d_{\\mathrm{out}}}$ computes\n\\begin{equation}\nu_j=\\sum_{i=1}^{d_{\\mathrm{in}}}\\phi_{j,i}(z_i),\\qquad j=1,\\dots,d_{\\mathrm{out}},\n\\label{eq:kanlayer}\n\\end{equation}\nwhere each $\\phi_{j,i}$ is learned. This added flexibility is the central motivation for our head: by\nshaping the activation itself, a KAN can represent the fine, non-linear relationships between deep features\nand dementia stage that a fixed-activation MLP captures only with many more parameters. The original KAN\nparameterizes each $\\phi$ with B-splines \\citep{liu2024kan}, but evaluating and rescaling spline bases is\ncomputationally costly. We instead adopt the radial-basis-function (RBF) formulation of \\citet{li2024fastkan},\nwhich is both faster and numerically more stable. A standard RBF network expresses a function as a weighted\nsum of localized kernels,\n\\begin{equation}\n\\mathrm{RBF}(z)=\\sum_{k=1}^{G} w_{k}\\,\\varphi\\!\\big(\\lVert z-c_k\\rVert\\big),\\qquad\n\\varphi(r)=\\exp\\!\\big(-r^{2}/h^{2}\\big),\n\\label{eq:rbf}\n\\end{equation}\nand FastKAN realizes each edge function as such an RBF expansion over a fixed grid $\\{c_k\\}_{k=1}^{G}$,\naugmented with a Sigmoid-Linear-Unit (SiLU) residual that supplies a smooth global component:\n\\begin{equation}\n\\phi(z)=w_{b}\\,\\mathrm{SiLU}(z)+\\sum_{k=1}^{G} w_{k}\\,\n\\exp\\!\\left(-\\frac{(z-c_k)^{2}}{h^{2}}\\right),\\qquad\n\\mathrm{SiLU}(z)=z\\,\\sigma(z),\n\\label{eq:fastkan}\n\\end{equation}\nwhere $\\sigma(\\cdot)$ is the logistic sigmoid, $h=(c_{\\max}-c_{\\min})/(G-1)$ is the grid spacing, and\n$w_b,\\{w_k\\}$ are trainable. To keep activations within the effective support of the fixed grid---the main\npractical failure mode of RBF-KANs---each KAN layer first applies layer normalization to its input. The head\nstacks two such layers with dropout for regularization, reducing the $768$-dimensional backbone features to\na hidden width of $128$ and then to $C$ logits, followed by a softmax,\n\\begin{equation}\n\\mathbf{o}=\\mathrm{KAN}_{2}\\!\\big(\\mathrm{dropout}(\\mathrm{KAN}_{1}(\\mathbf{z}))\\big),\\qquad\np_c=\\frac{\\exp(o_c)}{\\sum_{c'=1}^{C}\\exp(o_{c'})}.\n\\label{eq:head}\n\\end{equation}\nBecause the KAN replaces only the lightweight head rather than the backbone, the additional cost over a\nstandard linear classifier is modest (each edge stores $G+1$ scalars), keeping the model practical in\nstandard deep-learning frameworks. The structure of the KAN head used here is illustrated in\nFigure~\\ref{fig:kan_head}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{4.png}\n\\caption{KAN-based learnable-activation classification head. The 768-dimensional ConvNeXt feature vector is\nlayer-normalized and passed through two KAN layers ($768\\!\\to\\!128$ and $128\\!\\to\\!4$) with dropout in\nbetween and a final softmax over the four Alzheimer's stages. The inset contrasts a traditional MLP, with\nfixed ReLU activations and linear edges, against a KAN, in which every edge is a learnable function\n$\\phi(z)$ implemented as a sum of Gaussian RBFs over a fixed grid plus a SiLU residual\n(Eq.~\\ref{eq:fastkan}).}\n\\label{fig:kan_head}\n\\end{figure}\n\n\\subsection{Objective}\nThe soft targets produced by MixUp/CutMix are further regularized with label smoothing, which redistributes\na small mass $\\varepsilon$ uniformly over classes \\citep{szegedy2016rethinking},\n\\begin{equation}\ny_c^{\\mathrm{LS}}=(1-\\varepsilon)\\,y_c+\\frac{\\varepsilon}{C}.\n\\label{eq:ls}\n\\end{equation}\nLabel smoothing discourages over-confident logits and improves probability calibration, which is especially\ndesirable for clinical decision support; we use a modest $\\varepsilon$ because the mixing augmentation\nalready softens the targets. The model is trained with the categorical cross-entropy\n\\begin{equation}\n\\mathcal{L}=-\\sum_{c=1}^{C} y_c^{\\mathrm{LS}}\\,\\log p_c .\n\\label{eq:ce}\n\\end{equation}\n\n\\subsection{Optimization and two-phase training}\n\\label{subsec:opt}\nWe optimize with AdamW \\citep{loshchilov2019adamw}. Adam \\citep{kingma2015adam} maintains exponential moving\naverages of the gradient $g_t$ and its square,\n\\begin{equation}\nm_t=\\beta_1 m_{t-1}+(1-\\beta_1)\\,g_t,\\quad\nv_t=\\beta_2 v_{t-1}+(1-\\beta_2)\\,g_t^{2},\\quad\n\\hat{m}_t=\\frac{m_t}{1-\\beta_1^{t}},\\quad\n\\hat{v}_t=\\frac{v_t}{1-\\beta_2^{t}},\n\\label{eq:adammoments}\n\\end{equation}\nand AdamW decouples weight decay from this adaptive step, which generalizes better than folding the penalty\ninto the gradient as in coupled $L_2$ regularization:\n\\begin{equation}\n\\theta_{t}=\\theta_{t-1}-\\eta_{t}\\!\\left(\\frac{\\hat{m}_t}{\\sqrt{\\hat{v}_t}+\\epsilon}+\\lambda_{\\mathrm{wd}}\\,\\theta_{t-1}\\right),\n\\label{eq:adamw}\n\\end{equation}\nwhere $\\lambda_{\\mathrm{wd}}$ is the weight-decay coefficient. The learning rate follows a cosine schedule\nwith linear warm-up over $T_w$ steps and total budget $T$,\n\\begin{equation}\n\\eta_t=\n\\begin{cases}\n\\dfrac{t}{T_w}\\,\\eta_{\\max}, & t\\le T_w,\\\\[2.2mm]\n\\eta_{\\min}+\\dfrac{1}{2}\\left(\\eta_{\\max}-\\eta_{\\min}\\right)\\!\\left(1+\\cos\\dfrac{\\pi\\,(t-T_w)}{T-T_w}\\right), & t> T_w.\n\\end{cases}\n\\label{eq:cosine}\n\\end{equation}\nThe warm-up phase is important here because the randomly initialized KAN head produces large early\ngradients; ramping the learning rate from a small value prevents these from destabilizing the pretrained\nbackbone, while the subsequent cosine decay anneals smoothly toward a sharp minimum. Training proceeds in\ntwo phases for the same reason: (i) the backbone is frozen and only the KAN head is trained at a higher peak\nlearning rate, so the head can adapt to the fixed features without corrupting them; then (ii) the backbone\nis unfrozen and the whole network is fine-tuned at a much lower peak learning rate, allowing the features to\nspecialize to brain MRI without catastrophic forgetting. Early stopping on the validation loss with\nbest-weight restoration is used throughout to guard against overfitting.\n\n\\subsection{Test-time augmentation and metrics}\nAt inference we reduce prediction variance by averaging the output on the clean image with the outputs on\n$M$ lightly augmented copies, an inexpensive ensemble over views,\n\\begin{equation}\n\\bar{p}(x)=\\frac{1}{M+1}\\left(f(x)+\\sum_{m=1}^{M} f\\big(a_m(x)\\big)\\right),\n\\label{eq:tta}\n\\end{equation}\nwhere $a_m(\\cdot)$ denotes a random augmentation. Performance is reported with per-class precision, recall,\nand F1 \\citep{aslan2025jcma,aslan2025jastt},\n\\begin{equation}\n\\mathrm{P}=\\frac{TP}{TP+FP},\\quad\n\\mathrm{R}=\\frac{TP}{TP+FN},\\quad\nF_1=\\frac{2\\,\\mathrm{P}\\cdot \\mathrm{R}}{\\mathrm{P}+\\mathrm{R}},\n\\label{eq:prf}\n\\end{equation}\nand summarized by accuracy and the macro-averaged F1 \\citep{aslan2026mrl,manzari2025medvitv2},\n\\begin{equation}\n\\text{macro-}F_1=\\frac{1}{C}\\sum_{c=1}^{C} F_1^{(c)} .\n\\label{eq:macrof1}\n\\end{equation}\nWe emphasize the macro-average because it weights every stage equally and therefore reflects performance on\nthe clinically important minority classes rather than being dominated by the most frequent one. We also\nreport the mean one-vs-rest area under the receiver-operating-characteristic curve (ROC--AUC), a\nthreshold-independent measure of separability \\citep{aslan2025jcma}. In the ablation experiments that follow, we additionally\nreport balanced accuracy (which coincides with the standard accuracy on our balanced test set but is\nretained for consistency with other reports in the literature), the Matthews correlation coefficient\n(MCC), and Cohen's kappa~$\\kappa$ \\citep{gao2025msfkan}. MCC is defined for the multi-class case as\n\\begin{equation}\n\\mathrm{MCC}=\n\\frac{c\\,s-\\sum_{k}\\,t_k\\,p_k}\n     {\\sqrt{\\bigl(s^{2}-\\sum_{k}p_k^{2}\\bigr)\\bigl(s^{2}-\\sum_{k}t_k^{2}\\bigr)}} ,\n\\label{eq:mcc}\n\\end{equation}\nwhere $c$ is the total number of correctly classified samples, $s$ the total number of samples,\n$t_k$ the number of times class $k$ was truly present, and $p_k$ the number of times class $k$ was\npredicted; it takes values in $[-1,+1]$ and is known to be more informative than accuracy under residual\nclass imbalance \\citep{aslan2025jastt}. Cohen's kappa measures agreement between predictions and labels beyond what would be\nexpected by chance \\citep{manzari2025medvitv2},\n\\begin{equation}\n\\kappa=\\frac{p_o-p_e}{1-p_e} ,\n\\label{eq:kappa}\n\\end{equation}\nwith $p_o$ the observed agreement and $p_e$ the agreement expected under independent random labeling. To\nassess whether observed differences between competing models on the same test set are statistically\nsignificant we use McNemar's test with continuity correction: for each pair of classifiers we form the\ncontingency of examples that only one model classifies correctly and compare $\\chi^2=(|b-c|-1)^2/(b+c)$\nto a chi-square distribution with one degree of freedom~\\citep{mcnemar1947}.\n\n\\section{Results}\n\n\\subsection{Implementation details}\nModels were implemented in TensorFlow/Keras and trained on a single GPU. We used ConvNeXt-Tiny with ImageNet\nweights, input size $224\\times224$, and batch size $32$. The KAN head used a hidden width of $128$ and\n$G=8$ grid points per edge. Training used AdamW with decoupled weight decay $10^{-4}$, label smoothing\n$\\varepsilon=0.05$, a cosine schedule with one warm-up epoch (peak learning rate $10^{-3}$ for the head\nphase of $12$ epochs and $10^{-5}$ for the fine-tuning phase of up to $25$ epochs), MixUp with\n$\\alpha=0.2$ together with CutMix, and test-time augmentation with $M=4$. Following the protocol of\nSection~3.2, abundant classes were capped at $T=1{,}500$ and the validation and test sets were balanced at\n$V=E=73$ images per class; the training partition was balanced by oversampling to the largest class.\n\n\\subsection{Classification performance}\n\\label{sec:internal_results}\nTable~\\ref{tab:results} reports test performance on the balanced held-out set. ConvNeXt--KAN reaches\n$94.5\\%$ accuracy with a macro-averaged F1 of $0.944$ and a weighted F1 of $0.944$; the mean one-vs-rest\nROC--AUC is $0.991$. The moderate-dementia class is classified essentially perfectly, and mild dementia is\nrecognized with an F1 of $0.97$. The remaining error concentrates on the clinically hardest boundary:\nnon-demented recall is $0.82$, with the corresponding misclassifications falling mostly into the very-mild\ncategory (very-mild precision $0.87$), consistent with the near-normal appearance of very-mild disease.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Per-class and overall test performance of ConvNeXt--KAN on the balanced, held-out OASIS test set\n($73$ images per class). Values use test-time augmentation.}\n\\label{tab:results}\n\\begin{tabular}{lcccc}\n\\toprule\nClass & Precision & Recall & F1-score & Support \\\\\n\\midrule\nNon Demented        & 0.97 & 0.82 & 0.89 & 73 \\\\\nMild Demented       & 0.96 & 0.99 & 0.97 & 73 \\\\\nModerate Demented   & 1.00 & 1.00 & 1.00 & 73 \\\\\nVery Mild Demented  & 0.87 & 0.97 & 0.92 & 73 \\\\\n\\midrule\nAccuracy            & \\multicolumn{4}{c}{0.945\\quad(292 images)} \\\\\nMacro average       & 0.95 & 0.95 & 0.94 & 292 \\\\\nWeighted average    & 0.95 & 0.95 & 0.94 & 292 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nThe corresponding confusion matrices in absolute counts and row-normalized rates are shown in\nFigures~\\ref{fig:confusion} and~\\ref{fig:confusion_norm}. Per-class precision, recall, and F1 are visualized\nas a heatmap in Figure~\\ref{fig:classification_report} and as accuracy bars in\nFigure~\\ref{fig:per_class_acc}. The one-vs-rest ROC and precision--recall curves are reported in\nFigures~\\ref{fig:roc} and~\\ref{fig:pr}. Representative predictions on individual test slices and the global\nprediction-confidence distribution are shown in Figures~\\ref{fig:sample_predictions} and~\\ref{fig:confidence_dist}.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{Screenshot_48.png}\n\\caption{Confusion matrix (absolute counts) of ConvNeXt--KAN on the balanced held-out OASIS test set\n($73$ images per class, $292$ total). The diagonal dominance is strongest on moderate dementia (perfect\n$73/73$) and mild dementia ($72/73$); the only sizable off-diagonal cluster is non-demented misclassified as\nvery mild ($10/73$), reflecting the clinically subtlest boundary.}\n\\label{fig:confusion}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{Screenshot_49.png}\n\\caption{Row-normalized confusion matrix expressed as recall per true class. Moderate dementia is\nrecovered with $100\\%$ recall, mild dementia with $98.63\\%$, very mild with $97.26\\%$, and non-demented\nwith $82.19\\%$; the residual mass for non-demented again falls almost entirely on very mild ($13.70\\%$).}\n\\label{fig:confusion_norm}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{Screenshot_50.png}\n\\caption{Per-class precision, recall, and F1-score on the test set, shown as a heatmap. The metrics\nreproduce Table~\\ref{tab:results} and make the precision--recall asymmetry on the non-demented vs.\\\nvery-mild boundary visually explicit.}\n\\label{fig:classification_report}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.85\\textwidth]{Screenshot_51.png}\n\\caption{Per-class accuracy on the held-out test set. Moderate dementia is classified perfectly, while\nnon-demented---the clinically hardest class against very mild---attains $82.19\\%$.}\n\\label{fig:per_class_acc}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.85\\textwidth]{Screenshot_52.png}\n\\caption{One-vs-rest receiver-operating-characteristic curves for the four stages. The mean ROC--AUC is\n$0.991$; per-class AUCs are $0.980$ (non-demented), $0.999$ (mild), $1.000$ (moderate), and $0.985$\n(very mild).}\n\\label{fig:roc}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.85\\textwidth]{Screenshot_53.png}\n\\caption{One-vs-rest precision--recall curves for the four stages, with per-class average-precision values\nof $0.954$ (non-demented), $0.998$ (mild), $1.000$ (moderate), and $0.952$ (very mild). The two clinically\nadjacent classes occupy the lower-AP regime, consistent with the confusion-matrix pattern.}\n\\label{fig:pr}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{Screenshot_54.png}\n\\caption{Representative predictions on individual test slices, annotated with the true class, the predicted\nclass, and the softmax confidence. Correct predictions are concentrated at high confidence; the few errors\nfall on the visually subtle non-demented vs.\\ very-mild boundary.}\n\\label{fig:sample_predictions}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.85\\textwidth]{Screenshot_55.png}\n\\caption{Distribution of test-time prediction confidences, separated into correct (green) and incorrect\n(red) predictions. The model is well calibrated in the sense that incorrect predictions concentrate at\nlower confidences while correct predictions populate the high-confidence tail.}\n\\label{fig:confidence_dist}\n\\end{figure}\n\n\\subsection{Training dynamics}\nDuring the head-only phase the model rapidly exceeded chance as the KAN head adapted to the frozen\nConvNeXt features; during fine-tuning the validation accuracy rose further while the validation loss\ndecreased monotonically, with validation accuracy tracking or exceeding training accuracy, indicating no\noverfitting under the chosen regularization.\n\n\\subsection{Ablation study}\nTable~\\ref{tab:ablation} isolates the two main design choices. With a randomly initialized, frozen backbone\nthe network cannot learn discriminative features and collapses toward a single class ($0.35$ accuracy,\n$0.25$ macro-F1). Replacing the from-scratch giant backbone with a compact CNN that is trainable on small\ndata, but still under minority-capping, recovers a usable model ($0.72$ accuracy). Finally, pretrained\nConvNeXt features together with the expanded-data protocol of Section~3.2 yield the full model at $0.945$\naccuracy. Pretrained features and data utilization are therefore the dominant factors, with the KAN head\nproviding the learnable-activation decision boundary on top of those features.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Ablation on the effect of pretrained features and data utilization (balanced held-out test set).}\n\\label{tab:ablation}\n\\begin{tabular}{lcc}\n\\toprule\nConfiguration & Accuracy & Macro-F1 \\\\\n\\midrule\nRandom backbone, frozen (no pretraining)            & 0.35 & 0.25 \\\\\nCompact CNN, from scratch (minority-capped data)    & 0.72 & 0.71 \\\\\nConvNeXt--KAN, pretrained (expanded data)           & \\textbf{0.945} & \\textbf{0.944} \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{KAN versus MLP head on the same backbone}\n\\label{sec:head_ablation}\nTo isolate the contribution of the learnable-activation head from the contribution of the ConvNeXt\nbackbone, we compared the proposed KAN head against a conventional multilayer-perceptron (MLP)\nclassification head on the same ConvNeXt-Tiny backbone under an identical, matched training protocol. The\nMLP head uses the same hidden width ($128$), the same dropout schedule, and a GELU activation, so it\ndiffers from the KAN head only in that its activations are fixed rather than learned. Because a full sweep\nat the primary configuration ($25+50$ epochs) would have been prohibitively expensive when repeated for\nevery reviewer-requested comparison in this section, all head-to-head experiments below were run with a\nshortened but matched protocol of $10$ head epochs plus $20$ fine-tuning epochs; the primary $94.5\\%$\nnumber in Section~\\ref{sec:internal_results} continues to be produced with the full protocol using the\nKAN head. All other pipeline elements---MixUp/CutMix, label smoothing, cosine schedule, and test-time\naugmentation---were held fixed across the two heads.\n\nTable~\\ref{tab:head_ablation} reports the outcome. Under this matched-but-shortened protocol both heads\nreach broadly comparable performance: the KAN head achieves an accuracy of $0.8836$, macro-F1 $0.8805$,\nMCC $0.8486$, Cohen's kappa $0.8447$, and mean one-vs-rest ROC--AUC $0.9814$, while the MLP head reaches\naccuracy $0.8973$, macro-F1 $0.8974$, MCC $0.8648$, kappa $0.8630$, and ROC--AUC $0.9793$. The two heads\ntherefore exchange a small margin: the MLP is slightly ahead on the threshold-dependent metrics, while the\nKAN head is slightly ahead on the threshold-independent ROC--AUC, and neither margin passes the noise\nfloor. A McNemar test on the paired predictions returns $\\chi^2=0.409$ and $p=0.5224$ (with $b=9$ examples\nthat only the KAN head classifies correctly and $c=13$ that only the MLP head classifies correctly), so\nthe null hypothesis of equal predictive accuracy on this test set cannot be rejected at any conventional\nsignificance level. Figure~\\ref{fig:head_comparison} visualizes the five main metrics side by side.\n\nTwo observations are worth stating explicitly. First, the KAN head is not empirically dominant on this\nparticular internal test set at the shortened epoch budget; the practical case for it is instead that it\nprovides comparable performance at the cost of a small parameter overhead (Section~\\ref{sec:cost}) while\nadding learnable-activation capacity that may prove more advantageous at longer training regimes, larger\ndatasets, or when the classifier must model finer non-linearities than a MLP head can express with its\nfixed activations. Second, the primary $94.5\\%$ accuracy in Section~\\ref{sec:internal_results} is\nobtained with the full $25+50$ training protocol using the KAN head; the numbers in\nTable~\\ref{tab:head_ablation} are not directly comparable to that headline value and are reported here\nonly for head-to-head comparison.\n\n\\begin{table}[h!]\n\\centering\n\\caption{KAN versus MLP head on the same ConvNeXt-Tiny backbone under an identical, matched protocol\n($10$ head epochs $+$ $20$ fine-tuning epochs). The two heads exchange a small margin; the McNemar test on\npaired predictions confirms that the difference is not statistically significant. All values use\ntest-time augmentation.}\n\\label{tab:head_ablation}\n\\begin{tabular}{lcccccc}\n\\toprule\nHead & Accuracy & Macro-F1 & MCC & Kappa & ROC--AUC & Parameters \\\\\n\\midrule\nKAN (ours) & 0.8836 & 0.8805 & 0.8486 & 0.8447 & 0.9814 & $28.71\\,\\mathrm{M}$ \\\\\nMLP        & 0.8973 & 0.8974 & 0.8648 & 0.8630 & 0.9793 & $27.92\\,\\mathrm{M}$ \\\\\n\\midrule\n\\multicolumn{7}{l}{McNemar's test (KAN vs MLP): $\\chi^2=0.409$, $p=0.5224$, $b=9$, $c=13$.} \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.90\\textwidth]{fig_head_comparison.png}\n\\caption{Head-ablation summary on the ConvNeXt-Tiny backbone: accuracy, balanced accuracy, macro-F1,\nMatthews correlation coefficient, and Cohen's kappa for the KAN and MLP heads under the shortened matched\nprotocol described in Section~\\ref{sec:head_ablation}. The two heads exchange a small margin that is not\nstatistically significant (McNemar $p=0.5224$).}\n\\label{fig:head_comparison}\n\\end{figure}\n\n\\subsection{Backbone comparison: ConvNeXt-Tiny, ConvNeXt-Base, EfficientNet, DenseNet121, and Vision Transformer}\n\\label{sec:backbone_comparison}\nThe primary model uses a ConvNeXt-Tiny backbone on the grounds that its parameter count ($\\approx$28M) offers a\ngood capacity--regularization trade-off for the few-thousand-image training set available after the\nimbalance-aware split (Section~3.2). To examine whether stronger, larger backbones yield further improvements,\nwe conducted additional experiments using four alternative pretrained backbones on the same ConvNeXt-Tiny $+$ KAN\nhead pipeline (i.e., the KAN head is kept fixed and only the feature extractor is swapped): ConvNeXt-Base\n($\\approx$89M parameters), EfficientNetB4 \\citep{tan2019efficientnet} ($\\approx$19M parameters),\nDenseNet121 \\citep{huang2017densenet} ($\\approx$8M parameters), and a Vision Transformer (ViT-B/16)\n\\citep{dosovitskiy2021vit} ($\\approx$86M parameters). All experiments used the same shortened matched protocol\n(10 head epochs $+$ 20 fine-tuning epochs) and test-time augmentation as in Section~\\ref{sec:head_ablation}.\n\nTable~\\ref{tab:backbone_comparison} summarises the results. ConvNeXt-Tiny attains an accuracy of 0.8836 and\nmacro-F1 of 0.8805, and ConvNeXt-Base provides a modest improvement to 0.9007 accuracy and 0.8985 macro-F1.\nEfficientNetB4 performs comparably to ConvNeXt-Tiny (accuracy 0.8767, macro-F1 0.8751), while DenseNet121\ntrails slightly (accuracy 0.8596, macro-F1 0.8563). The Vision Transformer achieves 0.8699 accuracy\n(macro-F1 0.8682) under the same shortened protocol, suggesting it requires longer fine-tuning to reach its\npotential on this small dataset. The modest gains of ConvNeXt-Base over ConvNeXt-Tiny are consistent with\nthe expectation that larger backbones offer diminishing returns when the training set is small: the benefit\nof greater capacity is partly offset by increased overfitting risk, as reflected in the correspondingly\nhigher training-to-validation accuracy gaps. ConvNeXt-Tiny therefore remains the recommended backbone for\nthis setting, providing near-optimal performance at substantially lower memory and compute cost.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Backbone comparison on the KAN-head pipeline under the shortened matched protocol\n($10$ head epochs $+$ $20$ fine-tuning epochs). All values use test-time augmentation on the\nbalanced held-out test set.}\n\\label{tab:backbone_comparison}\n\\begin{tabular}{lccccc}\n\\toprule\nBackbone & Params (M) & Accuracy & Macro-F1 & MCC & ROC--AUC \\\\\n\\midrule\nConvNeXt-Tiny (ours) & 28.7  & 0.8836 & 0.8805 & 0.8486 & 0.9814 \\\\\nConvNeXt-Base        & 88.6  & 0.9007 & 0.8985 & 0.8680 & 0.9841 \\\\\nEfficientNetB4       & 19.3  & 0.8767 & 0.8751 & 0.8360 & 0.9798 \\\\\nDenseNet121          & 8.1   & 0.8596 & 0.8563 & 0.8138 & 0.9762 \\\\\nViT-B/16             & 86.4  & 0.8699 & 0.8682 & 0.8278 & 0.9789 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Comparison of imbalance-handling strategies}\n\\label{sec:imbalance_comparison}\nThe imbalance-aware training protocol in Section~3.2 combines a per-class cap on abundant classes with\nimage-space oversampling of minority classes on the training partition only, leaving the validation and\ntest partitions balanced and disjoint. Because the literature contains several well-established\nalternatives, we compared this strategy against three widely used baselines on the same ConvNeXt-Tiny\nbackbone, KAN head, and shortened protocol. The alternatives are: (i) synthetic minority oversampling\n(SMOTE)~\\citep{chawla2002smote}, applied not in pixel space---where the interpolated samples would be\nbiologically implausible---but in the ConvNeXt feature space, so that the KAN head is trained on\nSMOTE-balanced feature vectors; (ii) focal loss~\\citep{lin2017focal} with $\\gamma=2$ and $\\alpha=0.25$\napplied to the natural (unbalanced) training distribution; and (iii) class-balanced cross-entropy\nfollowing the effective-number reweighting of~\\citet{cui2019classbalanced} with $\\beta=0.9999$, also on\nthe natural training distribution. All four strategies were evaluated on the same fixed balanced test set.\n\nTable~\\ref{tab:imbalance} reports the outcome. The proposed image-space resampling strategy achieves the\nbest accuracy ($0.9007$), macro-F1 ($0.8999$), MCC ($0.8701$), and Cohen's kappa ($0.8676$). The\nclass-balanced cross-entropy is the strongest of the three alternatives, trailing our strategy by roughly\ntwo accuracy points ($0.8801$), and its difference from our approach is not statistically significant\n(McNemar $\\chi^2=1.786$, $p=0.1814$). Focal loss trails by about three accuracy points ($0.8699$) and its\ndifference from our strategy \\emph{is} statistically significant at the $0.05$ level (McNemar\n$\\chi^2=4.267$, $p=0.0389$). Feature-space SMOTE performs the worst by a wide margin ($0.8185$) despite\nproducing a numerically balanced feature-vector distribution, and the difference from our strategy is\nhighly significant (McNemar $\\chi^2=13.921$, $p=0.0002$); we attribute this gap to the fact that\ninterpolated feature vectors are only weakly constrained to lie on the manifold of real Alzheimer's MRI\nfeatures, so that the classifier partially fits synthetic points that are not representative of clinical\ndata. Figure~\\ref{fig:imbalance_strategies} summarizes the five metrics side by side.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Comparison of imbalance-handling strategies on the same ConvNeXt-Tiny + KAN backbone under the\nmatched shortened protocol. Statistical significance versus the proposed strategy is assessed with\nMcNemar's test on paired predictions.}\n\\label{tab:imbalance}\n\\begin{tabular}{lcccccc}\n\\toprule\nStrategy & Accuracy & Macro-F1 & MCC & Kappa & ROC--AUC & McNemar $p$ vs.\\ ours \\\\\n\\midrule\nOurs (image-space resample) & \\textbf{0.9007} & \\textbf{0.8999} & \\textbf{0.8701} & \\textbf{0.8676} & 0.9793 & --- \\\\\nFocal loss                  & 0.8699          & 0.8673          & 0.8282          & 0.8265          & 0.9802 & $0.0389^{\\ast}$ \\\\\nClass-balanced CE           & 0.8801          & 0.8804          & 0.8480          & 0.8402          & \\textbf{0.9817} & $0.1814$ \\\\\nSMOTE (feature space)       & 0.8185          & 0.8082          & 0.7661          & 0.7580          & 0.9701 & $0.0002^{\\ast\\ast\\ast}$ \\\\\n\\bottomrule\n\\multicolumn{7}{l}{$^{\\ast}p<0.05$;\\quad $^{\\ast\\ast\\ast}p<0.001$.} \\\\\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{fig_imbalance_strategies.png}\n\\caption{Imbalance-handling strategies compared on the same ConvNeXt-Tiny $+$ KAN pipeline: accuracy,\nbalanced accuracy, macro-F1, MCC, and Cohen's kappa for our image-space resampling strategy, focal loss,\nclass-balanced cross-entropy, and feature-space SMOTE. Our strategy leads on every metric except mean\none-vs-rest ROC--AUC, where the four methods are within $0.012$ of each other.}\n\\label{fig:imbalance_strategies}\n\\end{figure}\n\n\\subsection{Computational cost}\n\\label{sec:cost}\nBecause the KAN edge is a mixture of a Gaussian-RBF spline path and a SiLU-gated linear residual, it is\nnatural to ask what its cost is relative to a conventional dense layer. Table~\\ref{tab:cost} reports\ntotal parameters, classification-head-only parameters, per-image inference latency (measured after a\nwarm-up on the test batch pipeline), peak GPU memory during training, and end-to-end training time under\nthe matched shortened protocol. The KAN head accounts for $891{,}268$ parameters versus $98{,}948$ for the\nMLP head, so the KAN head is $\\approx 9\\times$ larger than the MLP head in absolute terms; however, both\nare dwarfed by the ConvNeXt-Tiny backbone, so the KAN--MLP difference amounts to only $792{,}320$\nadditional parameters and a $2.84\\%$ increase in the total model size. In practice, the extra RBF work is\nexecuted efficiently on the GPU, and per-image inference latency is actually marginally lower for the KAN\nhead ($5.37\\,\\mathrm{ms}$/image versus $5.60\\,\\mathrm{ms}$/image for the MLP head), while peak GPU memory\nis comparable ($4.50\\,\\mathrm{GiB}$ versus $4.81\\,\\mathrm{GiB}$) and end-to-end wall-clock training time\nis essentially identical ($65.6$ min versus $64.2$ min under the shortened protocol). We therefore\nconclude that the parameter overhead of the KAN head is small and its runtime overhead is negligible in\nthis pipeline. Figure~\\ref{fig:cost_comparison} visualizes these numbers.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Computational cost of the KAN head versus the MLP head on the same ConvNeXt-Tiny backbone.\nInference latency is measured per image after a warm-up pass on the test batch pipeline; training time\ncovers the shortened matched protocol ($10$ head epochs $+$ $20$ fine-tuning epochs).}\n\\label{tab:cost}\n\\begin{tabular}{lcc}\n\\toprule\nMetric & KAN (ours) & MLP \\\\\n\\midrule\nTotal parameters             & $28{,}711{,}396$          & $27{,}919{,}076$          \\\\\nHead-only parameters         & $891{,}268$               & $98{,}948$                \\\\\nInference latency (ms/image) & $5.37$                    & $5.60$                    \\\\\nPeak GPU memory (GiB)        & $4.50$                    & $4.81$                    \\\\\nTraining time (min)          & $65.6$                    & $64.2$                    \\\\\n\\midrule\nHead overhead (KAN$-$MLP)    & \\multicolumn{2}{c}{$+792{,}320$ params ($+2.84\\%$ of MLP total)} \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{fig_cost_comparison.png}\n\\caption{Computational cost of the KAN head versus the MLP head on the same ConvNeXt-Tiny backbone: total\nparameters (left), per-image inference latency (middle), and end-to-end training time under the\nshortened matched protocol (right). The KAN head adds $2.84\\%$ to the total parameter count without\nincreasing inference latency or wall-clock training time.}\n\\label{fig:cost_comparison}\n\\end{figure}\n\n\\subsection{Model interpretability with Grad-CAM and Score-CAM}\n\\label{sec:interpretability}\nTo assess which brain regions drive the model's predictions we visualized post-hoc saliency maps computed\nwith Grad-CAM~\\citep{selvaraju2017gradcam} and its gradient-free counterpart Score-CAM~\\citep{wang2020scorecam}.\nBoth methods attach to the deepest four-dimensional activation map of the ConvNeXt-Tiny backbone---a\n$7\\times 7\\times C$ tensor at $224\\times 224$ input resolution---and produce a spatial heatmap that is\nupsampled and blended with the input MRI slice. For Grad-CAM we use the log-probability of the target\nclass as the score, which is a standard fix that avoids the vanishing gradients that occur when the raw\nsoftmax output of a well-trained classifier saturates near one; for Score-CAM we mask the input with the\nupsampled activation of each of the top $24$ most active channels and weight the resulting per-channel\nimportance by the change in the class score. Because the backbone is nested inside the classification\nmodel as a sub-module, the naive Grad-CAM implementation---which builds a multi-output model directly\nfrom the nested layer's cached output tensor---fails silently by returning null gradients; we therefore\nreconstruct the forward pass through an explicit sub-model of the backbone that exposes both the target\nactivations and the pooled features and replay the KAN head on top, which keeps the target activations\ngradient-connected to the class logits.\n\nFigure~\\ref{fig:gradcam_scorecam} shows representative examples for two of the four classes on the\ninternal held-out test set, with the raw slice and the Grad-CAM and Score-CAM overlays displayed side by\nside. Two qualitative observations are worth stating. First, both saliency methods concentrate on the\ncortical rim and adjacent parenchymal regions rather than on background pixels or the skull outline,\nwhich is the pattern that would be expected if the model were relying on genuinely disease-relevant\nmorphology rather than on non-cerebral artefacts. Second, Grad-CAM and Score-CAM produce similar but\nnon-identical maps for the same slice, with Score-CAM tending to distribute attention more broadly\nbecause it aggregates over the $24$ top channels while Grad-CAM sharpens onto the specific spatial\nlocations whose gradients are largest for the target class; the two views are therefore complementary\nrather than redundant. A comprehensive quantitative evaluation of localization faithfulness (for example,\ndeletion and insertion curves, or an ROI-based analysis) is beyond the scope of the present manuscript\nand is left to future clinical follow-up.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=\\textwidth]{fig_gradcam_scorecam.png}\n\\caption{Representative post-hoc interpretability overlays produced with Grad-CAM (middle column of each\npair) and Score-CAM (right column of each pair) on individual held-out MRI slices, shown here for two of\nthe four Alzheimer's stages. Both methods concentrate attention on the cortical rim and adjacent\nparenchymal regions rather than on non-cerebral areas, and produce broadly consistent maps; Score-CAM\ndistributes attention more broadly by aggregating over the top $24$ channels of the deepest ConvNeXt\nfeature map, whereas Grad-CAM sharpens onto the locations whose gradients are largest for the target\nclass.}\n\\label{fig:gradcam_scorecam}\n\\end{figure}\n\n\\subsection{External validation on an independent dataset}\n\\label{sec:external_validation}\nTo probe whether the accuracy on OASIS transfers to a data distribution the model has never seen, we\nevaluated the trained ConvNeXt--KAN pipeline on an independent four-class Alzheimer's MRI collection\ndistributed on Kaggle,\\footnote{Preet Pal Singh, ``Alzheimer's Dataset (4 class of Images)'', Kaggle.\nAvailable at \\url{https://www.kaggle.com/datasets/preetpalsingh25/alzheimers-dataset-4-class-of-images}.\nAccessed for external validation in this study.} which uses the same clinical labels as OASIS\n(\\emph{Non Demented}, \\emph{Very Mild Demented}, \\emph{Mild Demented}, \\emph{Moderate Demented}) but is\nacquired under different imaging conditions and includes different subjects. The model was applied\n\\emph{as-is}, with no fine-tuning, no threshold recalibration, and no re-training, so that the numbers\nreported here measure only the out-of-distribution generalization of the classifier learned on OASIS. The\nsame preprocessing pipeline and the same four-crop test-time augmentation used in the internal evaluation\nwere applied to the external images. For a like-for-like comparison with Table~\\ref{tab:results}, the\nexternal set was balanced to $73$ images per class ($292$ images in total).\n\nTable~\\ref{tab:ext_results} summarizes the overall metrics. The model reaches a test-time-augmented\naccuracy of $0.6164$ on the external set, with an identical balanced accuracy of $0.6164$ (confirming\nthat the four classes contribute equally by construction) and a macro-averaged F1 of $0.5654$; because\nthe support is uniform, the weighted F1 coincides with the macro value at $0.5654$. Relative to the\n$94.5\\%$ obtained on the OASIS held-out set, this is a substantial drop of approximately $33$ percentage\npoints, in line with the magnitude of degradation that is repeatedly observed for MRI-based classifiers\nwhen they are transported across acquisition sites without any adaptation. Crucially, it is precisely\nthis gap---between an in-distribution number that is competitive with the literature and an\nout-of-distribution number that is markedly lower---that motivates the caution against single-dataset\nclaims of near-perfect Alzheimer's staging.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Zero-shot external validation of ConvNeXt--KAN on the independent four-class Alzheimer's MRI\ndataset (Kaggle, Preet Pal Singh). No fine-tuning is applied; test-time augmentation matches the internal\nevaluation.}\n\\label{tab:ext_results}\n\\begin{tabular}{lc}\n\\toprule\nMetric & Value \\\\\n\\midrule\nTest accuracy (TTA)     & 0.6164 \\\\\nBalanced accuracy       & 0.6164 \\\\\nMacro-averaged F1       & 0.5654 \\\\\nWeighted F1             & 0.5654 \\\\\nNumber of test images   & 292 (73 per class) \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nThe class-wise picture is more informative than the aggregate. Figures~\\ref{fig:ext_confusion}\nand~\\ref{fig:ext_confusion_norm} show the external confusion matrices in absolute counts and\nrow-normalized form, respectively. Three patterns are worth highlighting. First, the moderate-dementia\nclass continues to be recovered perfectly ($73/73$, $100\\%$ recall), replicating the internal-test\nbehavior and consistent with the fact that moderate atrophy produces the most visually distinctive MRI\nsignature and is therefore the least sensitive to acquisition-related domain shift. Second, non-demented\nrecall drops only modestly ($79.45\\%$ external versus $82.19\\%$ internal), suggesting that the model's\nnotion of a ``normal-appearing'' brain also generalizes reasonably well. Third, and by contrast, the two\nclinically intermediate stages absorb almost all of the additional error: mild-dementia recall collapses\nfrom $98.63\\%$ to $10.96\\%$, with the true mild-dementia scans redistributed mostly to\nvery-mild-demented ($43.84\\%$) and moderate-demented ($30.14\\%$), and very-mild-demented recall falls\nfrom $97.26\\%$ to $56.16\\%$, with the residual mass drifting toward non-demented ($24.66\\%$). This is\nconsistent with the fact that the visual differences between adjacent stages are subtle even for expert\nraters, so that the model's decision boundary in this narrow region is the one most sensitive to a\nchange in image intensity statistics, contrast, and slice selection between the two datasets.\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{Screenshot_161.png}\n\\caption{Confusion matrix (absolute counts) for zero-shot external validation of ConvNeXt--KAN on the\nindependent four-class Alzheimer's MRI dataset ($73$ images per class, $292$ total). Moderate dementia\nis again classified perfectly ($73/73$); most of the additional error concentrates on the two clinically\nintermediate stages, with mild-demented cases most frequently reassigned to very-mild-demented or\nmoderate-demented.}\n\\label{fig:ext_confusion}\n\\end{figure}\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.75\\textwidth]{Screenshot_162.png}\n\\caption{Row-normalized confusion matrix (recall per true class) on the external dataset. Moderate\ndementia is recovered with $100\\%$ recall and non-demented with $79.45\\%$; the intermediate stages\ndegrade more sharply, with mild-demented recall at $10.96\\%$ and very-mild-demented at $56.16\\%$. The\nsame qualitative pattern as the internal evaluation is preserved---errors cluster on adjacent\nstages---but the magnitude is larger, quantifying the cost of pure zero-shot transfer.}\n\\label{fig:ext_confusion_norm}\n\\end{figure}\n\nTaken together, the external evaluation both tempers the headline OASIS number and adds evidence for the\npaper's main methodological argument. The gross ordering across classes---moderate easiest,\nnon-demented next, then very-mild, then mild---is preserved between the two datasets, which is\nnon-trivial and suggests that the ConvNeXt--KAN features carry a genuine, if imperfect, signal about\ndisease stage rather than a purely dataset-specific shortcut. At the same time, the collapse of the\nintermediate classes under zero-shot transfer indicates that any clinical deployment of a model of this\nkind would require domain adaptation (for example, a small amount of fine-tuning on the target site, or\nsite-invariant training objectives) rather than direct reuse of the OASIS-trained weights, and it\nreinforces the case for reporting external, multi-site numbers alongside the internal test in future\nstudies.\n\n\\subsection{Novelty and positioning relative to existing KAN-based medical imaging studies}\n\\label{sec:novelty}\nTo clarify the contribution of ConvNeXt--KAN relative to the growing body of KAN-based medical imaging\nresearch, Table~\\ref{tab:novelty} summarises the key design differences between the proposed approach\nand the most closely related prior works. The central distinction is the \\emph{hybrid head design}: whereas\nMedKAN \\citep{yang2025medkan} builds a full KAN backbone with local and global information modules, and\nMedViTV2 \\citep{manzari2025medvitv2} replaces transformer feed-forward layers with KAN blocks throughout\nthe network, our approach retains a pretrained convolutional feature extractor (ConvNeXt) and uses a KAN\n\\emph{only as the classification head}. This design exploits the strong transfer-learned representations of\nConvNeXt while introducing learnable-activation decision boundaries at minimal additional cost---the KAN\nhead adds only 2.84\\% to total parameters and negligible inference latency (Section~\\ref{sec:cost}).\nFurthermore, to our knowledge, no prior KAN-based study has addressed the four-class OASIS\nAlzheimer's staging benchmark with an explicit imbalance-aware protocol (subject-level leakage control,\nclass-capped oversampling, balanced test set) or reported zero-shot external validation on an independent\ndataset, both of which are contributions of this work.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Comparison of ConvNeXt--KAN with existing KAN-based medical imaging studies. ``Head only''\nmeans the KAN replaces only the final classifier; ``Full backbone'' means KAN layers permeate the\nfeature extractor.}\n\\label{tab:novelty}\n\\footnotesize\n\\setlength{\\tabcolsep}{4pt}\n\\begin{tabular}{lllllll}\n\\toprule\nStudy & KAN scope & Backbone & Task & Dataset & Imbalance control & External validation \\\\\n\\midrule\n\\citet{liu2024kan}           & Full backbone  & KAN only      & Toy / scientific  & Various   & No  & No \\\\\n\\citet{yang2025medkan}       & Full backbone  & LIK+GIK       & Multi-disease clf & MedMNIST  & No  & No \\\\\n\\citet{bodner2024convkan}    & Conv layers    & ConvKAN       & General vision    & MNIST etc.& No  & No \\\\\n\\citet{manzari2025medvitv2}  & Transformer FF & MedViT        & Multi-disease clf & 27 sets   & Partial & No \\\\\n\\citet{gao2025msfkan}        & Multi-scale    & CNN+KAN       & Medical clf       & Various   & No  & No \\\\\n\\textbf{Ours (ConvNeXt--KAN)}& \\textbf{Head only} & \\textbf{ConvNeXt} & \\textbf{4-class AD staging} & \\textbf{OASIS+Kaggle} & \\textbf{Yes} & \\textbf{Yes} \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Discussion}\nThe results support the central hypothesis: a learnable-activation KAN head on a transfer-learned ConvNeXt\nbackbone yields accurate four-way Alzheimer's staging, with the largest residual error on the\nnon-demented/very-mild boundary that is also the most difficult for clinicians.\n\nThe reviewer-requested ablations in Sections~\\ref{sec:head_ablation}--\\ref{sec:interpretability} and the\nbackbone comparison and novelty analysis in Sections~\\ref{sec:backbone_comparison}--\\ref{sec:novelty} clarify\nwhere the model's headline number comes from and where it does not. The head-only comparison\n(Section~\\ref{sec:head_ablation}) shows that under a shortened matched protocol the KAN and MLP heads\nreach statistically indistinguishable accuracy on the internal test set (McNemar $p=0.52$); the KAN head\nis favoured on the threshold-independent ROC--AUC while the MLP head is favoured on threshold-dependent\nmetrics, and the two heads trade a small margin. This finding calibrates the case for the KAN head: at\nthe scale and epoch budget tested it is not empirically dominant, so the argument for adopting it rests\non its learnable-activation expressive capacity and its negligible runtime cost\n(Section~\\ref{sec:cost})---namely a $2.84\\%$ increase in total parameters, an essentially unchanged\ninference latency, and no measurable increase in wall-clock training time---rather than on a clear\naccuracy improvement in this regime. The imbalance-handling comparison in\nSection~\\ref{sec:imbalance_comparison} is more decisive: image-space resampling on the training\npartition dominates focal loss, class-balanced cross-entropy, and feature-space SMOTE across accuracy,\nmacro-F1, MCC, and kappa, with the SMOTE and focal-loss differences being statistically significant\n(McNemar $p=0.0002$ and $p=0.039$ respectively). Together with the leakage-controlled evaluation\nprotocol, this supports our choice of resampling as the imbalance strategy for the primary run. The\npost-hoc saliency analysis in Section~\\ref{sec:interpretability} shows that Grad-CAM and Score-CAM\nconcentrate attention on the cortical rim and adjacent parenchymal regions rather than on\nnon-cerebral areas, which is the qualitative pattern that would be expected if the model were relying on\ngenuinely disease-relevant morphology.\n\n\\label{sec:discussion_limits}\nFour limitations temper the\nheadline number. First, although our protocol removes image-duplication leakage by splitting before\noversampling and balancing the test set, the publicly distributed OASIS slices are not grouped by subject,\nso slices from one participant may still fall in different partitions; this can inflate accuracy and is a\nplausible explanation for the very high (often $\\geq 99\\%$) figures reported elsewhere on the same data.\nGenuinely patient-independent evaluation therefore requires a subject-level split, which we identify as the\nmost important next step. Second, the external evaluation reported in\nSection~\\ref{sec:external_validation} shows that zero-shot transfer to an independent four-class\nAlzheimer's MRI collection drops overall accuracy from $94.5\\%$ to $61.6\\%$, with the intermediate\nstages carrying most of the additional error. This is not a failure of the architecture---the moderate\nclass is still classified perfectly and the ordering of class difficulty is preserved---but it is a clear\nsignal that any clinical use would require domain adaptation to the target site rather than direct reuse\nof the OASIS-trained weights, and that broader multi-site validation remains a prerequisite for\nclinical claims.\n\nThird, the present study employs a single train/validation/test split rather than $k$-fold\ncross-validation. This is a deliberate practical choice: the extreme class imbalance in OASIS\n(moderate-dementia slices account for only $0.6\\%$ of the corpus) means that constructing $k$\nbalanced, non-overlapping folds of sufficient size for the minority class is not feasible without\nheavy oversampling \\emph{inside} each fold, which in turn reintroduces the leakage concern the\nevaluation protocol is designed to eliminate. Repeated hold-out evaluation (re-running the split\nwith different random seeds) would address variance estimation without this complication and is an\nimportant direction for future work. We also note that all reviewer-requested head comparisons,\nbackbone comparisons, and imbalance-handling comparisons in this manuscript are conducted under\na consistent, matched protocol on the same fixed test set, so the \\emph{relative} conclusions are\nunaffected by the use of a single split even if the absolute numbers carry some variance. Cross-validated\nestimates of the primary model's accuracy and macro-F1, obtained once a subject-level split\nbecomes feasible (i.e., when per-slice subject IDs are available), will be an important\ndeliverable for the follow-up study.\n\nFourth, the external validation uses an independent Alzheimer's MRI collection distributed on Kaggle\nrather than the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset that is commonly recommended\nin the literature. ADNI access requires an application and data-use agreement, which was not in place\nduring the preparation of this manuscript; the Kaggle collection was therefore used as the nearest\navailable independent four-class benchmark. We fully concur that ADNI validation is a scientifically\nimportant step and include it explicitly in our future-work plan. The external evaluation we do report\nnonetheless serves its intended purpose---it demonstrates measurable domain shift under zero-shot\ntransfer and argues for caution against single-dataset claims---and the Kaggle collection uses the\nsame four-class label set and was acquired from different subjects under different imaging conditions,\nmaking it a meaningful, if imperfect, proxy for out-of-distribution generalization.\n\n\\section{Conclusion}\n\nWe presented ConvNeXt--KAN, a model that combines a transfer-learned ConvNeXt backbone with a\nKolmogorov--Arnold Network classification head---an architecture in which the head's activations are learned\nrather than fixed---for multi-class staging of Alzheimer's disease from brain MRI. The KAN head, implemented\nefficiently with Gaussian radial basis functions, is designed to capture the subtle non-linear texture and\natrophy patterns that conventional MLP heads model poorly, and it is trained with a robustness-oriented\nrecipe (MixUp and CutMix, label smoothing, AdamW, a cosine schedule with warm-up, and test-time\naugmentation) together with a data strategy that exploits far more of the imbalanced OASIS collection while\nevaluating on a fixed, balanced, leakage-controlled test set. The model achieved $94.5\\%$ accuracy, a\nmacro-F1 of $0.944$, and a mean ROC--AUC of $0.991$ on the internal test set, and an ablation confirmed\nthat pretrained features and expanded data are the principal contributors. A zero-shot evaluation on an\nindependent four-class Alzheimer's MRI collection reached $61.6\\%$ accuracy and a macro-F1 of $0.565$\nwithout any fine-tuning, with moderate dementia still recovered perfectly and the intermediate stages\ncarrying most of the domain-shift error---evidence that the learned features generalize partially but\nthat domain adaptation would be required for clinical reuse of the OASIS-trained weights. Beyond the\nnumbers, the study contributes a transparent treatment of data utilization and evaluation, including an\nexplicit account of subject-level leakage as a confound in prior work and a quantified external\ncomparison. A backbone comparison (Section~\\ref{sec:backbone_comparison}) confirms that ConvNeXt-Tiny offers\nthe best capacity--regularization trade-off in this data regime: ConvNeXt-Base provides a small gain\n(+0.017 accuracy) at three times the parameter count, while EfficientNetB4, DenseNet121, and ViT-B/16 all\ntrail ConvNeXt-Tiny under matched conditions. A comparative novelty table (Section~\\ref{sec:novelty})\npositions ConvNeXt--KAN within the growing body of KAN-based medical imaging literature and highlights\nthe unique combination of hybrid head design, imbalance-aware protocol, and external validation that\ndistinguishes this work. Future work will (i) adopt a subject-level split for patient-independent evaluation and use repeated\n$k$-fold cross-validation once subject-level grouping information is available; (ii) validate on ADNI and\nother multi-site clinical cohorts to establish genuine cross-site generalizability; (iii) explore\nConvNeXt-Base as the backbone with domain-adaptation objectives; (iv) add probability calibration and\nadditional gradient-based explanation to improve clinical trust; and (v) investigate quantitative\nlocalization faithfulness metrics (deletion/insertion curves, ROI-based analysis) for a more rigorous\nassessment of model interpretability.\n\n\\section*{Conflict of Interest Statement}\nThe authors declare that the research was conducted in the absence of any commercial or financial\nrelationships that could be construed as a potential conflict of interest.\n\n\\section*{Author Contributions}\nAll authors contributed to the conception and design of the study. [First Author] implemented the models and\nexperiments and wrote the first draft; [Second Author] contributed to the clinical interpretation and\nevaluation protocol; [Third Author] supervised the work and revised the manuscript. All authors read and\napproved the submitted version. (Please update with author initials before submission.)\n\n\\section*{Funding}\nNo specific funding was received for this work. (Update with grant numbers if applicable.)\n\n\\section*{Acknowledgments}\nThe authors thank the Open Access Series of Imaging Studies (OASIS) for making the imaging data available.\n\n\\section*{Data Availability Statement}\nTwo publicly available datasets are analyzed in this study. Model development, internal training, and the\nheld-out test evaluation use the OASIS cross-sectional MRI collection \\citep{marcus2007oasis}, distributed\nin a four-class form on Kaggle. The external, zero-shot evaluation reported in\nSection~\\ref{sec:external_validation} uses the independent ``Alzheimer's Dataset (4 class of Images)''\ncollection distributed on Kaggle by Preet Pal Singh, available at\n\\url{https://www.kaggle.com/datasets/preetpalsingh25/alzheimers-dataset-4-class-of-images}.\n\n\\bibliographystyle{Frontiers-Harvard}\n\\bibliography{test}\n\\end{document}",
      "tex_filename": "frontiers.tex",
      "bib_content": "@article{Paul2026,\n  title={KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction},\n  author={Nirodh Paul and Md. Mahedi Hassan and Sumnoon Ferdous and Md. Masuqul Haque and Mir Mohammad Azad},\n  journal={Frontiers in Education},\n  doi={10.3389/feduc.2026.2804599},\n  year={2026}\n}\n",
      "source_dir": "/journals/sociology/articles/10.3389/fsoc.2026.2804691/source",
      "tex_file": "/journals/sociology/articles/10.3389/fsoc.2026.2804691/source/article.tex",
      "bib_file": "/journals/sociology/articles/10.3389/fsoc.2026.2804691/source/references.bib",
      "updated_at": "2026-11-07T12:11:34Z",
      "created_at": "2026-11-07T11:19:12Z"
    },
    {
      "title": "KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction",
      "authors": [
        {
          "name": "Nirodh Paul",
          "affiliations": [
            "1"
          ],
          "is_corresponding": false,
          "affil_str": "1",
          "initials": "NP"
        },
        {
          "name": "Md. Mahedi Hassan",
          "affiliations": [
            "2"
          ],
          "is_corresponding": false,
          "affil_str": "2",
          "initials": "MH"
        },
        {
          "name": "Sumnoon Ferdous",
          "affiliations": [
            "3"
          ],
          "is_corresponding": false,
          "affil_str": "3",
          "initials": "SF"
        },
        {
          "name": "Md. Masuqul Haque",
          "affiliations": [
            "4"
          ],
          "is_corresponding": false,
          "affil_str": "4",
          "initials": "MH"
        },
        {
          "name": "Mir Mohammad Azad",
          "affiliations": [
            "5"
          ],
          "is_corresponding": false,
          "affil_str": "5",
          "initials": "MA"
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh"
        },
        {
          "index": "2",
          "text": "Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh"
        },
        {
          "index": "3",
          "text": "Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh"
        },
        {
          "index": "4",
          "text": "Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh"
        },
        {
          "index": "5",
          "text": "Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh"
        }
      ],
      "corr_author": "",
      "corr_email": "kotpiuznd141@hotmail.com",
      "abstract": "Employee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov\u2013Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds incremental value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12% positive prevalence) under a nested 5{\u00d7}5-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC (0.8485 \u00b1 0.0266) and F1 (0.5945). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by +0.0114 (p = 0.0036, paired t-test; Wilcoxon minimum p = 0.0625, n=5 folds), PR-AUC by +0.0188, and F1 by +0.0698 on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the 0.0114 AUC gain\u2014achieved with only 237 positive cases\u2014against its practical screening benefit (3.7\u00d7 enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov\u2013Arnold networks provide distinct diversity that may benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.",
      "keywords": "employee attrition; Kolmogorov\u2013Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning",
      "doi": "10.3389/feduc.2026.8922077",
      "article_url_path": "/journals/education/articles/10.3389/feduc.2026.8922077/abstract",
      "journal_slug": "education",
      "journal": "Frontiers in Education",
      "journal_abbrev": "Front. Educ.",
      "section": "Sec. Higher Education",
      "banner": "/assets/images/journals/education-banner.png",
      "issn": "2504-284X",
      "impact_factor": "2.6",
      "citescore": "4.3",
      "received": "2026-10-20",
      "accepted": "2026-11-01",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
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      "id": "art_1230645",
      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Revised manuscript: KASTLE-X \u2014 Major Revision addressing Reviewers 1, 2, and 3\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%% Version 3.4 Generated 2022/06/14 %%%\n\\documentclass[utf8]{FrontiersinHarvard}\n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\\usepackage{amsmath,amssymb,booktabs,array,xcolor}\n\n\\linenumbers\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\\def\\firstAuthorLast{Author {et~al.}}\n\\def\\Authors{Nirodh Paul\\,$^{1}$, Md. Mahedi Hassan\\,$^{2}$, Sumnoon Ferdous\\,$^{3}$, Md. Masuqul Haque\\,$^{4}$ and Mir Mohammad Azad\\,$^{5}$}\n\\def\\Address{$^{1}$Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh \\\\\n$^{2}$Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh \\\\\n$^{3}$Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh \\\\\n$^{4}$Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh \\\\\n$^{5}$Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh}\n\n\\def\\corrAuthor{}\n\\def\\corrEmail{kotpiuznd141@hotmail.com}\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title[KASTLE-X for Employee Attrition Prediction]{KASTLE-X: Incremental Value of Kolmogorov--Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction}\n\n\\author[\\firstAuthorLast]{\\Authors}\n\\address{}\n\\correspondance{}\n\\extraAuth{}\n\n\\maketitle\n\n%-------------------------------------------------------------------\n\\begin{abstract}\n\\section{}\n\nEmployee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov--Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds \\emph{incremental} value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12\\% positive prevalence) under a nested $5{\\times}5$-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC ($0.8485 \\pm 0.0266$) and F1 ($0.5945$). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by $+0.0114$ ($p = 0.0036$, paired $t$-test; Wilcoxon minimum $p = 0.0625$, $n=5$ folds), PR-AUC by $+0.0188$, and F1 by $+0.0698$ on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the $0.0114$ AUC gain---achieved with only 237 positive cases---against its practical screening benefit ($3.7\\times$ enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov--Arnold networks provide distinct diversity that \\emph{may} benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.\n\n\\tiny\n \\keyFont{ \\section{Keywords:} employee attrition; Kolmogorov--Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning}\n\\end{abstract}\n\n\n%===================================================================\n\\section{Introduction}\n%===================================================================\n\n\\subsection{Research Context and Practical Motivation}\n\nVoluntary employee turnover is among the costliest operational events an organization can experience. Replacement expenditures are estimated at 50\\%--200\\% of a departing employee's annual salary \\citep{shrm_replacement_cost}, encompassing direct recruitment and onboarding costs as well as indirect costs from lost institutional knowledge and disrupted team cohesion. In large organizations, aggregate replacement costs readily reach tens of millions of dollars annually. Predictive analytics applied to routine HR records therefore represents a high-value operational intervention: identifying employees with elevated attrition risk in advance enables targeted engagement programs, compensation adjustments, or career-development conversations at a fraction of the replacement cost.\n\n\\subsection{Technical Challenges}\n\nThe machine-learning framing of attrition prediction is a binary classification task on a small, heterogeneous, highly imbalanced tabular dataset. Three structural properties make it genuinely challenging. First, the positive class is scarce: in the widely used IBM HR Analytics benchmark, only 237 of 1{,}470 employees (16.12\\%) left \\citep{ibm_dataset}. Second, the feature space mixes ordinal Likert scales, categorical job descriptors, and continuous financial variables whose marginal predictive power is modest after accounting for correlations. Third, the label contains substantial irreducible noise from personal events invisible in HR records, setting a genuine Bayes error floor. These properties cap achievable F1 at values that may seem moderate in absolute terms but represent genuine predictive value relative to the no-skill baseline.\n\n\\subsection{Methodological Gap}\n\nThe literature on attrition prediction is characterized by two concurrent weaknesses. First, published evaluations frequently report inflated performance because synthetic minority oversampling \\citep{chawla_smote} is applied before the train--test split, allowing synthetic copies of minority test samples to appear in training data \\citep{rahman_review}. Second, no published study has systematically examined whether Kolmogorov--Arnold Networks (KANs) \\citep{liu_kan}---a recently proposed architecture with learnable polynomial edge functions---add useful architectural diversity to stacking ensembles of conventional tabular learners. Architectural diversity is the primary mechanism through which stacking exceeds its constituent base learners \\citep{kuncheva_whitaker}, and dominant gradient-boosted decision tree (GBDT) variants in current pools often have prediction correlations exceeding 0.9, leaving limited room for meta-learner exploitation.\n\n\\subsection{Research Objectives}\n\nThis study addresses four objectives:\n\\begin{enumerate}\n  \\item[\\textbf{O1}] Establish a leakage-free benchmark of 20 individual classifiers spanning all major tabular algorithmic families on the engineered IBM HR dataset.\n  \\item[\\textbf{O2}] Develop KAN-Bag, a seed-bagged Chebyshev-polynomial KAN classifier, and quantify the separate contributions of the KAN architecture, seed bagging, and feature engineering through ablation.\n  \\item[\\textbf{O3}] Evaluate whether KAN-Bag provides statistically meaningful incremental value when added to a heterogeneous stacking ensemble (KASTLE-X vs.\\ Stacking-LR without KAN).\n  \\item[\\textbf{O4}] Characterize the practical limitations of the findings, including the single-dataset scope, small sample size, and implications for responsible HR deployment.\n\\end{enumerate}\n\n\\subsection{Contributions}\n\nAgainst these objectives, the specific contributions are: (i) \\emph{KAN-Bag}: a seed-bagged Chebyshev-polynomial KAN tabular classifier that achieves the highest individual AUC among 20 compared classifiers; (ii) \\emph{KASTLE-X}: a KAN-augmented stacking ensemble with a class-weighted logistic meta-learner, demonstrated to improve over the non-KAN stacking baseline on all five outer folds ($p=0.0036$); (iii) twelve leakage-free, domain-motivated engineered features confirmed by mutual-information analysis; (iv) a component ablation isolating the contributions of KAN architecture, seed bagging, and feature engineering; and (v) the most comprehensive honest evaluation of the IBM HR attrition benchmark to date, covering 20 individual models, 6 ensemble variants, 7 performance metrics, calibration analysis, statistical tests with explicitly bounded claims, and SHAP interpretability.\n\nThe remainder of the paper is organized as follows. Section~\\ref{sec:related} reviews related work. Section~\\ref{sec:methods} presents the dataset, exploratory analysis, feature engineering, KAN architecture, KASTLE-X framework, hyperparameter optimization, and evaluation protocol. Section~\\ref{sec:results} presents experimental results. Section~\\ref{sec:discussion} discusses findings, limitations, ethical considerations, and future directions. Section~\\ref{sec:conclusion} concludes.\n\n%===================================================================\n\\section{Literature Review}\\label{sec:related}\n%===================================================================\n\n\\subsection{Employee Attrition Prediction}\n\nEarly computational approaches to employee turnover used logistic regression and survival analysis. The democratization of the IBM HR Analytics dataset catalyzed a shift toward ML experimentation, with subsequent studies applying support vector machines, decision trees, random forests, gradient-boosting machines, and neural networks. \\citet{rahman_review} found that gradient-boosted ensembles---particularly XGBoost \\citep{chen_xgboost} and LightGBM \\citep{ke_lightgbm}---consistently produced the highest cross-validated AUC values (typically 0.80--0.87) when evaluation protocols were correctly specified.\n\nA pervasive concern is data leakage through synthetic oversampling. When SMOTE \\citep{chawla_smote} is applied before the train--test split, synthetic copies of test-set minority instances appear in training data, producing optimistic estimates. Under honest within-fold resampling on the IBM benchmark, F1 values of 0.45--0.55 are typical; published values of 0.80--0.90 in studies using pre-split SMOTE are leakage artifacts. The present study applies no resampling and restricts all processing to training partitions.\n\nMore recent work has explored deep learning for tabular attrition prediction. TabNet \\citep{arik_tabnet} uses sequential attention to select relevant features at each step. However, benchmarks such as \\citet{grinsztajn_trees} consistently find that well-tuned GBDTs match or outperform neural tabular architectures on small-to-medium datasets, a finding attributable to the inductive biases of tree ensembles: robustness to irrelevant features, implicit feature selection, and resistance to overparameterization. Explainability has emerged as a central concern in HR analytics; SHAP \\citep{lundberg_shap} provides consistent, locally additive feature attributions with game-theoretic foundations.\n\nRecent literature has also begun examining the impact of class-imbalance strategies in HR classification. \\citet{alqarni_power_bi_2025} demonstrated that ML models with power BI dashboards for attrition can aid managerial decision-making, and \\citet{bibliometric_attrition_2025} provided a bibliometric synthesis of ML methods for employee attrition prediction, identifying gradient boosting and neural networks as the most frequently applied approaches. \\citet{slr_attrition_2024} conducted a systematic literature review of quantitative attrition models, confirming that ensemble methods dominate recent publications but that rigorous leakage-free protocols remain underrepresented.\n\n\\subsection{Ensemble Learning and Stacking}\n\nBagging reduces variance by averaging predictions over bootstrap subsamples; boosting reduces bias through additive residual fitting; stacking \\citep{wolpert_stacking} trains a meta-learner on out-of-fold predictions from heterogeneous base learners. The meta-learner learns the optimal combination rather than assuming a fixed rule.\n\nDiversity of base learners is central to stacking's benefit: if all base learners make correlated errors, the meta-learner has no information to correct them. \\citet{kuncheva_whitaker} formalized this diversity--accuracy trade-off, showing that ensembles benefit most when base-learner errors are conditionally independent. Practical stacking implementations achieve diversity by combining learners with different inductive biases---linear models, kernel machines, tree ensembles, and neural architectures. However, GBDT variants dominate current tabular stacking pools, and their prediction correlations often exceed 0.9. Super-learner theory \\citep{vanderlaan_superlearner} provides asymptotic justification: under regularity conditions, the cross-validated stacked ensemble converges to the oracle model minimizing expected loss among all convex combinations of base learners.\n\n\\subsection{Kolmogorov--Arnold Networks and Tabular Deep Learning}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957, arnold_1963} establishes that any continuous $f:[0,1]^n\\to\\mathbb{R}$ can be written as a finite composition of continuous univariate functions and additions. \\citet{liu_kan} proposed KANs as a neural architecture inspired by this theorem, replacing fixed activations on nodes with learnable univariate functions on edges parameterized by B-splines. Subsequent work has explored alternative bases: \\citet{bozorgasl_wavkan} used wavelets; Chebyshev polynomial bases offer computational advantages through a stable three-term recurrence.\n\nThe current empirical state of KAN research for tabular classification reveals a nuanced picture. Early evidence from \\citet{liu_kan} demonstrated that KANs can match or exceed MLPs on scientific and regression tasks with fewer parameters. However, the broader tabular deep-learning literature---as surveyed in \\citet{grinsztajn_trees} and synthesized in \\citet{arik_tabnet}---consistently finds that GBDTs retain an advantage on small-to-medium tabular datasets due to their ability to handle irregular feature distributions, categorical variables, and uninformative features without specialized architectural inductive biases. KANs, like MLPs, lack these inductive biases, making their advantage domain-dependent. On small, imbalanced HR datasets---the focus of this paper---their behavior as standalone predictors and as ensemble components has received little systematic attention. This study contributes such an assessment.\n\n\n%===================================================================\n\\section{Materials and Methods}\\label{sec:methods}\n%===================================================================\n\n\\noindent\\textbf{Glossary.}\n\\begin{center}\n\\begin{tabular}{lp{0.72\\linewidth}}\n\\toprule\n\\textbf{Term} & \\textbf{Definition} \\\\\n\\midrule\nLeakage-free feature engineering & Features constructed as row-wise transformations that depend only on the individual observation and universal constants, with no reference to other rows, group statistics, or the target variable. \\\\\nNested cross-validation & A two-level CV protocol in which the outer loop evaluates model performance and the inner loop handles all model selection and tuning, ensuring outer test folds are never touched during optimization. \\\\\nMeta-learner & The second-level model in a stacking ensemble that is trained on the out-of-fold predictions of base learners and learns the optimal combination of their outputs. \\\\\nOOF (out-of-fold) predictions & Predictions on held-out inner validation folds; every training example receives a prediction from a model that was never fitted on it. \\\\\nKAN-Bag & The seed-bagged Chebyshev-polynomial KAN classifier proposed in this study. \\\\\nKASTLE-X & The full stacking ensemble combining KAN-Bag with seven conventional Bayesian-optimized learners. \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\n\\subsection{Dataset and Preprocessing}\n\nThe IBM HR Analytics Employee Attrition \\& Performance dataset \\citep{ibm_dataset} contains 1{,}470 employee records with 35 attributes. The binary target \\textsc{Attrition} takes value \\textit{Yes} for 237 records (16.12\\%) and \\textit{No} for 1{,}233 records (83.88\\%), yielding an imbalance ratio of approximately $5.2{:}1$. The dataset has zero missing values and zero duplicated rows. Four non-informative constant columns (\\textsc{EmployeeCount}, \\textsc{Over18}, \\textsc{StandardHours}, \\textsc{EmployeeNumber}) were removed, leaving 30 raw attributes spanning five conceptual domains: (a) demographics, (b) compensation and incentives, (c) job context, (d) attitudinal Likert scales, and (e) tenure history. Seven categorical features were one-hot encoded without reference-category dropping, producing a 51-feature matrix from raw attributes. Models requiring standardized inputs (logistic regression, SVM, KAN) applied a \\textsc{StandardScaler} fitted exclusively on the training partition of each fold.\n\n\\textbf{Important contextual note.} The IBM HR Analytics dataset is a synthetic release used widely as a benchmark. The present study treats it as such: all findings are bounds on a single synthetic benchmark, and generalization to other organizations requires external validation.\n\n\\subsection{Leakage-Free Feature Engineering}\n\nTwelve domain-motivated engineered features were constructed as strictly row-wise transformations, using only the individual row's attributes and universal constants. This makes data leakage structurally impossible: the same mapping applies to any training or test partition. Let $\\text{OT}=\\mathbb{1}\\{\\textsc{OverTime}=\\textit{Yes}\\}$ and $\\varepsilon=10^{-6}$. Intuitively, these features encode quantities that standard employee records capture indirectly: for instance, $f_1$ measures income adequacy relative to job level (detecting undercompensation), $f_5$ measures career stagnation, and $f_{10}$ captures the interaction of overtime demand with work--life balance (an overtime stress signal). Such constructions reflect the job-demands--resources model from organizational psychology.\n\n\\begin{align}\nf_1 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{JobLevel}+\\varepsilon}, &\nf_2 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{Age}+\\varepsilon}, &\nf_3 &= \\frac{\\textsc{YearsAtCompany}}{\\textsc{TotalWorkingYears}+1} \\label{eq:fe1}\\\\\nf_4 &= \\frac{\\textsc{TotalWorkingYears}}{\\textsc{NumCompaniesWorked}+1}, &\nf_5 &= \\frac{\\textsc{YearsSinceLastPromotion}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe2}\\\\\nf_6 &= \\frac{\\textsc{YearsWithCurrManager}}{\\textsc{YearsAtCompany}+1}, &\nf_7 &= \\frac{\\textsc{YearsInCurrentRole}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe3}\\\\\nf_8 &= \\tfrac{1}{4}(\\textsc{JobSat}+\\textsc{EnvSat}+\\textsc{RelSat}+\\textsc{WLB}), &\nf_9 &= \\textsc{JobInvolvement}\\times\\textsc{JobSatisfaction} \\label{eq:fe4}\\\\\nf_{10} &= \\text{OT}\\times(5-\\textsc{WLB}), &\nf_{11} &= \\textsc{DistanceFromHome}\\times\\text{OT}, &\nf_{12} &= \\frac{\\textsc{PercentSalaryHike}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe5}\n\\end{align}\n\nTogether with the 51 raw encoded features, the final design matrix is $\\mathbf{X}\\in\\mathbb{R}^{1470\\times 63}$.\n\n\\subsection{Component Contribution Ablation}\n\nTo isolate the contributions of the KAN architecture, seed bagging, Bayesian optimization, and feature engineering---as requested by Reviewer 3---we conducted a four-condition ablation on a fixed 5-fold stratified CV (Table~\\ref{tab:ablation_components}). Condition A uses raw (non-engineered) features, a single-seed KAN-Net without bagging, and no Bayesian optimization. Each subsequent condition adds one component. This design supports attributing performance increments to specific methodological choices rather than to the composite package.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Component contribution ablation ($5$-fold stratified CV, mean $\\pm$ std on AUC). Each row adds one component to the prior row to isolate its contribution.}\\label{tab:ablation_components}\n\\begin{tabular}{llccc}\n\\toprule\n\\textbf{Condition} & \\textbf{Components Active} & \\textbf{AUC} & \\textbf{F1} & $\\boldsymbol{\\Delta}$ \\textbf{AUC vs.\\ A} \\\\\n\\midrule\nA & Raw features, single-seed KAN-Net & $0.7931 \\pm 0.031$ & $0.4853$ & --- \\\\\nB & + Engineered features ($f_1$--$f_{12}$) & $0.8227 \\pm 0.016$ & $0.5426$ & $+0.0296$ \\\\\nC & + Seed bagging ($S=3$, no BO) & $0.8391 \\pm 0.022$ & $0.5712$ & $+0.0460$ \\\\\nD & + Bayesian hyperparameter optimization & $0.8485 \\pm 0.027$ & $0.5945$ & $+0.0554$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nThe ablation shows that feature engineering contributes $+0.030$ AUC, seed bagging a further $+0.016$, and Bayesian optimization a further $+0.009$. These increments are additive and independently meaningful. The KAN architecture itself is best assessed by comparing Condition A against the analogous MLP-based condition (Table~\\ref{tab:zoo}), where KAN-Net (single seed) outperforms the MLP by $0.0394$ AUC on the same engineered features.\n\n\\subsection{Chebyshev-KAN Tabular Classifier}\n\n\\subsubsection{Architecture}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957} states that any continuous $f:[0,1]^n\\to\\mathbb{R}$ admits\n\\begin{equation}\\label{eq:ka_theorem}\nf(x_1,\\ldots,x_n) = \\sum_{q=0}^{2n} \\Phi_q\\!\\left(\\sum_{p=1}^{n}\\varphi_{q,p}(x_p)\\right)\n\\end{equation}\nfor continuous univariate functions $\\varphi_{q,p}$ and $\\Phi_q$. Intuitively, this guarantees that the network can, in principle, represent complex nonlinear interactions between employee features and attrition risk without requiring an exponentially growing number of parameters.\n\nMotivated by~\\eqref{eq:ka_theorem}, an $L$-layer KAN with width vector $[n_0,\\ldots,n_L]$ applies at each layer $\\ell$ a learnable univariate edge function $\\varphi_{\\ell,j,i}$ to each input coordinate $x_{\\ell,i}$ and sums:\n\\begin{equation}\\label{eq:kan_layer}\nx_{\\ell+1,j} = \\sum_{i=1}^{n_\\ell} \\varphi_{\\ell,j,i}(x_{\\ell,i}), \\quad j=1,\\ldots,n_{\\ell+1}.\n\\end{equation}\n\nWe parameterize each edge function using a Chebyshev polynomial basis of degree $D$. The Chebyshev polynomials $T_0,T_1,\\ldots,T_D$ satisfy the three-term recurrence\n\\begin{equation}\\label{eq:cheby_rec}\nT_0(u)=1,\\quad T_1(u)=u,\\quad T_k(u) = 2u\\,T_{k-1}(u) - T_{k-2}(u),\n\\end{equation}\nwhich admits stable batched computation. To ensure inputs lie in $[-1,1]$ (the polynomial's natural domain), a $\\tanh$ squashing is applied before basis expansion. Intuitively, this allows the network to model monotone and non-monotone response curves (e.g., the U-shaped relationship between tenure and attrition risk) through a small number of low-degree coefficients, which standard ReLU networks would require many hidden units to approximate.\n\nA ChebyKAN layer with input dimension $d_\\text{in}$, output dimension $d_\\text{out}$, and degree $D$ maintains a coefficient tensor $\\mathbf{C}\\in\\mathbb{R}^{d_\\text{in}\\times d_\\text{out}\\times(D+1)}$:\n\\begin{equation}\\label{eq:chebykan}\n\\text{out}_{j} = \\sum_{i=1}^{d_\\text{in}} \\sum_{k=0}^{D} \\mathbf{C}_{i,j,k}\\, T_k\\!\\big(\\tanh(x_i)\\big),\n\\end{equation}\nimplemented as a single \\textsc{einsum} contraction. The KAN-Net classifier is a two-layer ChebyKAN network:\n\\begin{equation}\\label{eq:kannet}\n\\mathbf{h} = \\text{LayerNorm}\\big(\\text{ChebyKAN}_{63\\to 24,D=3}(\\mathbf{x})\\big), \\quad \\hat{y} = \\sigma\\big(\\text{ChebyKAN}_{24\\to 1,D=3}(\\mathbf{h})\\big),\n\\end{equation}\nwith total parameter count $63\\cdot 24\\cdot 4 + 24\\cdot 1\\cdot 4 = 6{,}240$ trainable weights (excluding layer-norm), roughly half the comparable MLP ($64\\to 32\\to 1$, $\\approx 11{,}300$ parameters).\n\n\\subsubsection{Training Objective}\n\nGiven $N$ training examples with labels $y_i\\in\\{0,1\\}$ and class-imbalance ratio $r=N_-/N_+$, we minimize the class-weighted binary cross-entropy:\n\\begin{equation}\\label{eq:bce}\n\\mathcal{L} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{y}_i + (1-y_i)\\log(1-\\hat{y}_i)\\right],\\quad w_i = \\begin{cases} r & y_i=1 \\\\ 1 & y_i=0 \\end{cases}\n\\end{equation}\nFor the IBM benchmark $r\\approx 5.2$, upweighting minority-class contributions. Parameters are updated with Adam \\citep{kingma_adam} ($\\eta=5\\times 10^{-3}$, $L_2$ decay $\\lambda=10^{-3}$), full-batch for up to 600 epochs with early stopping on a stratified 20\\% internal validation split (patience 50 epochs, minimum improvement $10^{-4}$ AUC).\n\n\\subsubsection{Seed Bagging (KAN-Bag)}\n\nA single KAN-Net exhibited nontrivial initialization-dependent variance. KAN-Bag averages probabilities from $S=3$ KAN-Net instances trained with distinct seeds $s\\in\\{42,202,777\\}$:\n\\begin{equation}\\label{eq:kanbag}\n\\hat{p}_{\\text{KAN-Bag}}(\\mathbf{x}) = \\frac{1}{S}\\sum_{s=1}^{S} \\hat{y}_s(\\mathbf{x}).\n\\end{equation}\nBy the bias--variance decomposition, if $S$ models have equal bias and pairwise error correlation $\\rho$, bagged variance is $\\sigma^2/S\\cdot[1+(S-1)\\rho]$, decreasing approximately as $1/S$ for small $\\rho$. In the component ablation (Table~\\ref{tab:ablation_components}), seed bagging raised AUC from $0.8227$ to $0.8391$---a contribution comparable to feature engineering---demonstrating that initialization variance is a primary challenge for small-dataset KAN training.\n\n\\subsection{KASTLE-X: KAN-Augmented Stacking Ensemble}\n\n\\subsubsection{Base-Learner Pool}\n\nKASTLE-X maintains a pool $\\mathcal{P}$ of $K=8$ base learners: $\\mathcal{P} = \\{\\text{LightGBM}^\\star, \\text{XGBoost}^\\star, \\text{CatBoost}, \\text{HistGB}, \\text{RF}, \\text{ExtraTrees}, \\text{LR}, \\text{KAN-Bag}\\}$, where $\\star$ denotes per-fold Bayesian optimization. This spans histogram-based gradient boosting \\citep{ke_lightgbm, chen_xgboost}, ordered boosting \\citep{prokhorenkova_catboost}, variance-reduction ensembles, a linear boundary model, and the proposed KAN architecture, maximizing conditional independence of base-learner errors. An architecture diagram of the complete KASTLE-X pipeline---from raw data through feature engineering, base learners, OOF meta-features, and meta-learner---is shown in Figure~\\ref{fig:pipeline}.\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{f4992235-9dd8-4ac0-8094-9c3d78ca4a1e.png}\n\\end{center}\n\\caption{KASTLE-X architecture diagram. Raw features are combined with 12 leakage-free engineered features to form a 63-feature design matrix. In each outer fold, base learners generate out-of-fold (OOF) meta-features on the training partition; the logistic meta-learner is trained on these OOF features. At inference time all base learners are refit on the full training partition and the meta-learner combines their predictions. The KAN-Bag component is highlighted to distinguish it from the conventional learners.}\\label{fig:pipeline}\n\\end{figure}\n\n\\subsubsection{Leakage-Free Out-of-Fold Meta-Features}\n\nLet $\\mathcal{D}=\\{(\\mathbf{x}_i,y_i)\\}_{i=1}^{N}$ be the training data for a given outer fold. Partition $\\mathcal{D}$ into $K_{\\text{in}}=5$ inner folds. For each inner fold $t$ with training set $\\mathcal{D}_t^{\\text{tr}}$ and validation set $\\mathcal{D}_t^{\\text{va}}$, train each base learner $b_k$ on $\\mathcal{D}_t^{\\text{tr}}$ and predict on $\\mathcal{D}_t^{\\text{va}}$. Each training example receives a prediction from a model never fit on it, yielding the leakage-free meta-feature matrix $\\mathbf{Z}\\in\\mathbb{R}^{N\\times K}$:\n\\begin{equation}\\label{eq:oof}\nZ_{i,k} = b_k^{\\,\\backslash t(i)}(\\mathbf{x}_i), \\quad i=1,\\ldots,N,\\ k=1,\\ldots,K.\n\\end{equation}\n\n\\subsubsection{Class-Weighted Logistic Meta-Learner}\n\nThe meta-learner is a class-balanced logistic regression with $L_2$ regularization:\n\\begin{equation}\\label{eq:meta_lr}\n\\hat{p}_{\\text{meta}}(\\mathbf{z}) = \\sigma(\\mathbf{w}^\\top\\mathbf{z} + b), \\quad \\mathbf{w}\\in\\mathbb{R}^K,\\ b\\in\\mathbb{R},\n\\end{equation}\n\\begin{equation}\\label{eq:meta_loss}\n\\mathcal{L}_{\\text{meta}} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{p}_{\\text{meta}}(\\mathbf{z}_i) + (1-y_i)\\log(1-\\hat{p}_{\\text{meta}}(\\mathbf{z}_i))\\right] + \\lambda\\lVert\\mathbf{w}\\rVert_2^2.\n\\end{equation}\nLogistic regression is chosen as the meta-learner for four reasons: (i) convexity guarantees convergence; (ii) the weight vector $\\mathbf{w}$ provides directly interpretable attribution of each base learner's marginal contribution; (iii) under super-learner theory \\citep{vanderlaan_superlearner}, a logistic meta-learner is asymptotically optimal among convex combinations for log-loss risk; and (iv) empirically, on this dataset size ($N\\approx 1{,}176$ training samples per outer fold), logistic meta-learners outperformed MLP and KAN-residual meta-learners. Note that the logistic meta-learner operates on the base learners' predicted \\emph{probabilities} rather than on original features; as such, its weight vector explains the ensemble-level combination, not feature-level influence, which is the role of the TreeSHAP analysis in Section~\\ref{sec:shap}.\n\n\\subsubsection{F1-Optimal Threshold Selection}\n\nThe default threshold $\\tau=0.5$ is inappropriate at 16\\% prevalence. For each outer fold, the threshold is selected on inner-OOF meta-predictions:\n\\begin{equation}\\label{eq:thresh}\n\\tau^* = \\argmax_{\\tau\\in(0,1)}\\ \\text{F1}\\!\\left(\\mathbf{y},\\mathbb{1}\\{\\hat{p}_{\\text{meta}}(\\mathbf{z})\\geq\\tau\\}\\right).\n\\end{equation}\nBecause $\\tau^*$ is computed entirely within the training partition, it introduces no optimistic bias.\n\n\\subsection{Hyperparameter Optimization}\n\nLightGBM and XGBoost are optimized per outer fold using Optuna's Tree-structured Parzen Estimator (TPE) \\citep{akiba_optuna}. The complete hyperparameter search spaces and final selected values are provided in Table~\\ref{tab:hyperparams}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Hyperparameter search spaces and representative final selected values for LightGBM and XGBoost (per outer fold via Optuna TPE, 25 trials, 3-fold inner CV AUC objective). All other pool members use fixed configurations listed in the Supplementary Material.}\\label{tab:hyperparams}\n\\footnotesize\n\\begin{tabular}{lllr}\n\\toprule\n\\textbf{Model} & \\textbf{Hyperparameter} & \\textbf{Search Range} & \\textbf{Typical Selected} \\\\\n\\midrule\nLightGBM & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 390 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.063 \\\\\n & \\texttt{num\\_leaves} & $[15, 63]$ (int) & 31 \\\\\n & \\texttt{min\\_child\\_samples} & $[10, 60]$ (int) & 24 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.82 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.75 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 0.48 \\\\\n\\midrule\nXGBoost & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 420 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.055 \\\\\n & \\texttt{max\\_depth} & $[3, 8]$ (int) & 5 \\\\\n & \\texttt{min\\_child\\_weight} & $[1, 10]$ (int) & 3 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.79 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.71 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 1.24 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nRegarding imbalance handling: boosting models (LightGBM, XGBoost, CatBoost, HistGB) incorporate class-imbalance handling natively via their split-gain criteria (through \\texttt{scale\\_pos\\_weight} or \\texttt{class\\_weight}), and no additional resampling is applied because our ablation (Table~\\ref{tab:imbalance}) confirmed that SMOTE/ADASYN degraded AUC for GBDT learners on this dataset. For tree ensembles (RF, ExtraTrees) and logistic regression, explicit \\texttt{class\\_weight=\"balanced\"} is used. We note that no multiple-comparison correction is applied to the statistical tests in Table~\\ref{tab:stats}, as each comparison is a pre-specified pairwise test of a distinct ensemble configuration against KASTLE-X; we report raw $p$-values and encourage readers to interpret them conservatively.\n\n\\subsection{Evaluation Protocol}\n\nThe protocol is fully nested to eliminate all known leakage pathways. The outer loop uses 5-fold stratified CV (seed 42); the inner loop uses 5-fold stratified CV within each outer training partition. Within a single outer fold: (i) outer split; (ii) inner-OOF generation of $\\mathbf{Z}$; (iii) Optuna tuning on the training partition; (iv) meta-learner training on $(\\mathbf{Z},\\mathbf{y}^{\\text{tr}})$; (v) isotonic calibration on OOF predictions (calibrated variant only); (vi) $\\tau^*$ selection via~\\eqref{eq:thresh}; (vii) refit of all base learners on the full training partition; (viii) test inference; (ix) metric computation. Steps (ii)--(vi) are strictly confined to $\\mathcal{D}^{\\text{tr}}$; only step (ix) accesses $\\mathcal{D}^{\\text{te}}$.\n\nReported metrics: ROC-AUC, PR-AUC, F1, balanced accuracy, MCC, and Brier score as mean $\\pm$ std across five outer folds. Fold-wise AUC differences are assessed with the paired $t$-test and Wilcoxon signed-rank test ($n=5$; the attainable Wilcoxon minimum is $p=0.0625$).\n\n\n%===================================================================\n\\section{Results}\\label{sec:results}\n%===================================================================\n\n\\subsection{Exploratory Analysis}\n\nThe class distribution is markedly imbalanced (Figure~\\ref{fig:class}). Kernel-density comparisons show leavers concentrated at younger ages, lower incomes, and shorter tenures (Figure~\\ref{fig:kde}). Categorical breakdowns show elevated attrition among overtime workers, frequent travelers, single employees, and sales roles; ordinal engagement variables show monotone gradients where attrition declines as satisfaction and involvement increase (Figures~\\ref{fig:cat} and~\\ref{fig:ordinal}). Risk is front-loaded in the first one to three years (Figure~\\ref{fig:tenure}). Mutual-information analysis confirms that six of the twelve engineered features appear in the top-20 ranking, with \\textsc{OverTimeStress} ($f_{10}$) the second most informative feature overall (Figures~\\ref{fig:mi} and~\\ref{fig:mieng}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.5\\linewidth]{Screenshot_77.png}\n\\end{center}\n\\caption{Class distribution of the attrition label (prevalence $= 0.161$, $n=1{,}470$).}\\label{fig:class}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_78.png}\n\\end{center}\n\\caption{Kernel-density comparisons of key numeric features by attrition status.}\\label{fig:kde}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_76.png}\n\\end{center}\n\\caption{Attrition rates across categorical features.}\\label{fig:cat}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_79.png}\n\\end{center}\n\\caption{Attrition rate across ordinal engagement variables.}\\label{fig:ordinal}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_75.png}\n\\end{center}\n\\caption{Attrition rate by tenure bins.}\\label{fig:tenure}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_73.png}\n\\end{center}\n\\caption{Top-20 features by mutual information, including engineered features.}\\label{fig:mi}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_74.png}\n\\end{center}\n\\caption{Mutual-information ranking restricted to the twelve engineered features.}\\label{fig:mieng}\n\\end{figure}\n\n\\subsection{Imbalance-Handling Ablation}\n\nA preliminary ablation evaluated four strategies on a fixed LightGBM learner under 5-fold stratified CV (Table~\\ref{tab:imbalance}). No resampling achieved the highest AUC ($0.8125$), consistent with prior findings that SMOTE distorts GBDT decision boundaries. Main experiments therefore use no resampling for boosting models and balanced class weights for tree ensembles and logistic regression.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Imbalance-handling ablation on a fixed LightGBM learner ($5$-fold, mean $\\pm$ std). All resampling is applied strictly within training folds.}\\label{tab:imbalance}\n\\begin{tabular}{lccc}\n\\toprule\n\\textbf{Strategy} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} \\\\\n\\midrule\nNone (raw) & $0.8125 \\pm 0.023$ & $0.5639 \\pm 0.047$ & $0.4358 \\pm 0.050$ \\\\\nClass weighting (balanced) & $0.8109 \\pm 0.029$ & $0.5612 \\pm 0.055$ & $0.4547 \\pm 0.044$ \\\\\nSMOTE (within-fold) & $0.8014 \\pm 0.019$ & $0.5490 \\pm 0.052$ & $0.4350 \\pm 0.047$ \\\\\nADASYN (within-fold) & $0.8035 \\pm 0.019$ & $0.5547 \\pm 0.047$ & $0.4376 \\pm 0.033$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Individual Model Benchmark}\n\nTwenty classifiers were evaluated on the 63-feature design matrix under 5-fold stratified CV (Table~\\ref{tab:zoo}, Figure~\\ref{fig:zoo}). \\textbf{KAN-Bag achieves the highest AUC ($0.8485$), PR-AUC ($0.6354$), F1 ($0.5945$), balanced accuracy ($0.7780$), and MCC ($0.5131$) among all 20 individual classifiers.} Minority-class precision is 0.630 and minority-class recall is 0.562. The second-best on AUC is LDA ($0.8267$). All four GBDT variants are outperformed by KAN-Bag at the zoo-evaluation stage; they perform substantially better as pool members after per-fold Bayesian tuning.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Individual model benchmark on engineered features ($5$-fold, mean $\\pm$ std). Best value per metric in bold. Minority-class (attrition=Yes) Prec./Rec.\\ are for information at the F1-optimal threshold.}\\label{tab:zoo}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Model} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Min.Prec} & \\textbf{Min.Rec} \\\\\n\\midrule\n\\textbf{KAN-Bag (proposed)} & $\\mathbf{0.8485 \\pm 0.027}$ & $\\mathbf{0.6354 \\pm 0.057}$ & $\\mathbf{0.5945 \\pm 0.044}$ & $\\mathbf{0.7780 \\pm 0.020}$ & $\\mathbf{0.5131 \\pm 0.053}$ & $\\mathbf{0.630}$ & $0.562$ \\\\\nLDA & $0.8267 \\pm 0.026$ & $0.6300 \\pm 0.059$ & $0.5548 \\pm 0.076$ & $0.7126 \\pm 0.042$ & $0.5032 \\pm 0.081$ & $0.544$ & $0.566$ \\\\\nLogistic Regression & $0.8247 \\pm 0.024$ & $0.5952 \\pm 0.044$ & $0.4857 \\pm 0.015$ & $0.7400 \\pm 0.017$ & $0.3801 \\pm 0.024$ & $0.471$ & $0.501$ \\\\\nLinear SVM & $0.8235 \\pm 0.026$ & $0.6015 \\pm 0.049$ & $0.3703 \\pm 0.068$ & $0.6153 \\pm 0.027$ & $0.4007 \\pm 0.064$ & $0.641$ & $0.262$ \\\\\nRandom Forest & $0.8227 \\pm 0.041$ & $0.5775 \\pm 0.068$ & $0.4471 \\pm 0.044$ & $0.6522 \\pm 0.020$ & $0.4115 \\pm 0.063$ & $0.468$ & $0.428$ \\\\\nKAN-Net (single) & $0.8227 \\pm 0.016$ & $0.5790 \\pm 0.059$ & $0.5426 \\pm 0.061$ & $0.7508 \\pm 0.043$ & $0.4483 \\pm 0.076$ & $0.547$ & $0.539$ \\\\\nSVM (RBF) & $0.8200 \\pm 0.026$ & $0.5799 \\pm 0.039$ & $0.4797 \\pm 0.025$ & $0.6664 \\pm 0.014$ & $0.4540 \\pm 0.024$ & $0.502$ & $0.458$ \\\\\nAdaBoost & $0.8198 \\pm 0.029$ & $0.5965 \\pm 0.056$ & $0.4895 \\pm 0.057$ & $0.6733 \\pm 0.026$ & $0.4494 \\pm 0.073$ & $0.491$ & $0.489$ \\\\\nExtra Trees & $0.8146 \\pm 0.025$ & $0.5729 \\pm 0.066$ & $0.5063 \\pm 0.051$ & $0.6903 \\pm 0.021$ & $0.4366 \\pm 0.074$ & $0.508$ & $0.504$ \\\\\nCatBoost & $0.8115 \\pm 0.026$ & $0.5934 \\pm 0.037$ & $0.4262 \\pm 0.051$ & $0.6409 \\pm 0.024$ & $0.4160 \\pm 0.041$ & $0.434$ & $0.419$ \\\\\nBagging (DT) & $0.8039 \\pm 0.031$ & $0.5431 \\pm 0.034$ & $0.4362 \\pm 0.051$ & $0.6470 \\pm 0.023$ & $0.3990 \\pm 0.071$ & $0.440$ & $0.433$ \\\\\nHistGB & $0.8035 \\pm 0.025$ & $0.5507 \\pm 0.048$ & $0.4286 \\pm 0.047$ & $0.6435 \\pm 0.024$ & $0.4013 \\pm 0.035$ & $0.435$ & $0.423$ \\\\\nGradient Boosting & $0.8029 \\pm 0.016$ & $0.5528 \\pm 0.015$ & $0.4372 \\pm 0.060$ & $0.6509 \\pm 0.031$ & $0.3918 \\pm 0.045$ & $0.439$ & $0.435$ \\\\\nLightGBM & $0.8022 \\pm 0.036$ & $0.5521 \\pm 0.048$ & $0.4227 \\pm 0.064$ & $0.6414 \\pm 0.030$ & $0.3980 \\pm 0.050$ & $0.425$ & $0.420$ \\\\\nXGBoost & $0.7999 \\pm 0.026$ & $0.5570 \\pm 0.042$ & $0.4211 \\pm 0.039$ & $0.6390 \\pm 0.016$ & $0.3962 \\pm 0.062$ & $0.423$ & $0.419$ \\\\\nGaussian NB & $0.7841 \\pm 0.041$ & $0.4775 \\pm 0.037$ & $0.4562 \\pm 0.024$ & $0.7226 \\pm 0.022$ & $0.3431 \\pm 0.035$ & $0.349$ & $0.659$ \\\\\nMLP & $0.7833 \\pm 0.042$ & $0.5438 \\pm 0.057$ & $0.4591 \\pm 0.053$ & $0.6695 \\pm 0.028$ & $0.3717 \\pm 0.062$ & $0.460$ & $0.459$ \\\\\nKNN & $0.7775 \\pm 0.044$ & $0.4681 \\pm 0.060$ & $0.1874 \\pm 0.048$ & $0.5515 \\pm 0.014$ & $0.2768 \\pm 0.037$ & $0.387$ & $0.120$ \\\\\nQDA & $0.7516 \\pm 0.035$ & $0.4326 \\pm 0.056$ & $0.4524 \\pm 0.019$ & $0.6923 \\pm 0.016$ & $0.3320 \\pm 0.025$ & $0.345$ & $0.662$ \\\\\nDecision Tree & $0.6666 \\pm 0.038$ & $0.3498 \\pm 0.020$ & $0.4154 \\pm 0.033$ & $0.6697 \\pm 0.027$ & $0.2825 \\pm 0.045$ & $0.409$ & $0.422$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_72.png}\n\\end{center}\n\\caption{Individual model benchmark ($5$-fold stratified CV). KAN-Bag attains the highest AUC among all twenty individual classifiers.}\\label{fig:zoo}\n\\end{figure}\n\n\\subsection{Ensemble Comparison}\n\nNested-CV results for six ensemble variants are presented in Table~\\ref{tab:ensembles}. KASTLE-X achieves AUC $0.8449\\pm0.020$, PR-AUC $0.6570\\pm0.051$, and F1 $0.5831\\pm0.035$. Minority-class recall is 59.5\\% and minority-class precision is 62.4\\%.\n\n\\textbf{Reframing KASTLE-X's contribution (per Reviewer 2).} KAN-Bag is the strongest individual classifier, and KASTLE-X does not surpass KAN-Bag on AUC ($0.8449$ vs.\\ $0.8485$). The contribution of KASTLE-X lies elsewhere: the ensemble improves over the non-KAN stacking baseline (Stacking-LR no KAN, $0.8335$ AUC) by $+0.0114$ AUC and $+0.0698$ F1, and it achieves this consistently on all five outer folds. KASTLE-X should therefore be understood not as a universally superior predictor, but as evidence that \\emph{KAN augmentation within stacking provides incremental value beyond a conventional pool of seven learners}. Whether a practitioner prefers KAN-Bag (simpler, slightly higher AUC) or KASTLE-X (higher F1, better PR-AUC) depends on the operational cost structure.\n\n\\begin{table}[h!]\n\\centering\n\\caption{KASTLE-X ensemble comparison, nested $5$-fold CV (mean $\\pm$ std). Model complexity is shown as approximate total parameter count / training time relative to Stacking-LR (no KAN).}\\label{tab:ensembles}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Method} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Brier} & \\textbf{Rel.\\,Time} \\\\\n\\midrule\n\\textbf{KASTLE-X (proposed)} & $\\mathbf{0.8449 \\pm 0.020}$ & $\\mathbf{0.6570 \\pm 0.051}$ & $\\mathbf{0.5831 \\pm 0.035}$ & $0.7574 \\pm 0.030$ & $\\mathbf{0.5054 \\pm 0.036}$ & $0.1424 \\pm 0.021$ & $1.0\\times$ \\\\\nKASTLE-X + isotonic & $0.8410 \\pm 0.021$ & $0.6276 \\pm 0.056$ & $0.5831 \\pm 0.035$ & $0.7574 \\pm 0.030$ & $0.5054 \\pm 0.036$ & $\\mathbf{0.0918 \\pm 0.010}$ & $1.0\\times$ \\\\\nKASTLE-X KANres meta & $0.8422 \\pm 0.026$ & $0.6543 \\pm 0.049$ & $0.5665 \\pm 0.058$ & $0.7483 \\pm 0.041$ & $0.4865 \\pm 0.063$ & $0.1414 \\pm 0.029$ & $1.1\\times$ \\\\\nRank-average voting & $0.8388 \\pm 0.025$ & $0.6382 \\pm 0.061$ & $0.5665 \\pm 0.043$ & $0.7452 \\pm 0.034$ & $0.4844 \\pm 0.049$ & $0.2344 \\pm 0.007$ & $0.9\\times$ \\\\\nSoft voting & $0.8404 \\pm 0.023$ & $0.6338 \\pm 0.058$ & $0.5215 \\pm 0.025$ & $0.6918 \\pm 0.012$ & $0.4764 \\pm 0.048$ & $0.0956 \\pm 0.008$ & $0.9\\times$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $0.8335 \\pm 0.021$ & $0.6382 \\pm 0.055$ & $0.5133 \\pm 0.032$ & $\\mathbf{0.7541 \\pm 0.026}$ & $0.4135 \\pm 0.044$ & $0.1550 \\pm 0.012$ & $0.7\\times$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_71.png}\n\\end{center}\n\\caption{ROC curves for KASTLE-X and comparison ensembles on pooled OOF predictions.}\\label{fig:roc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_70.png}\n\\end{center}\n\\caption{Precision--recall curves; dashed line marks the prevalence baseline (0.161).}\\label{fig:pr}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_69.png}\n\\end{center}\n\\caption{Fold-wise AUC across five outer folds. KASTLE-X exceeds Stacking-LR (no KAN) on every fold.}\\label{fig:foldauc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.65\\linewidth]{Screenshot_68.png}\n\\end{center}\n\\caption{Ensemble learning curve (diagnostic). Validation AUC continues to improve modestly with additional training examples, indicating performance is not saturated at $n=1{,}470$.}\\label{fig:learning}\n\\end{figure}\n\n\\subsection{Ablation and Statistical Tests}\n\n\\subsubsection{KAN Augmentation Ablation}\n\nKASTLE-X vs.\\ Stacking-LR (no KAN) on fold-wise AUC:\n\n\\begin{center}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Fold} & \\textbf{KASTLE-X} & \\textbf{Stacking-LR (no KAN)} \\\\\n\\midrule\n1 & 0.8327 & 0.8277 ($+0.0050$) \\\\\n2 & 0.8356 & 0.8209 ($+0.0147$) \\\\\n3 & 0.8746 & 0.8642 ($+0.0104$) \\\\\n4 & 0.8567 & 0.8451 ($+0.0116$) \\\\\n5 & 0.8251 & 0.8097 ($+0.0154$) \\\\\n\\midrule\nMean $\\pm$ SD & $0.8449\\pm0.020$ & $0.8335\\pm0.021$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\nThe AUC difference is positive on every fold; paired $t(4)=5.85$, $p=0.0036$ (95\\% CI for $\\Delta$AUC: $[0.0057,\\ 0.0172]$). The Wilcoxon signed-rank test yields $p=0.0625$ (minimum attainable with $n=5$ pairs). The discrepancy between the two tests is expected: with only five pairs, the paired $t$-test leverages the magnitude of differences whereas the Wilcoxon test uses only signs; both are consistent with a real but small effect, and inferential claims are explicitly qualified by $n=5$ in this paper.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Fold-wise statistical comparison ($n=5$ folds). Paired $t$-test and Wilcoxon signed-rank $p$-values on AUC. 95\\% confidence intervals for mean fold-wise $\\Delta$AUC are shown.}\\label{tab:stats}\n\\begin{tabular}{lcccc}\n\\toprule\n\\textbf{Comparison (KASTLE-X vs.)} & $\\boldsymbol{\\Delta}$\\textbf{AUC} & \\textbf{95\\% CI} & \\textbf{Paired $t$ $p$} & \\textbf{Wilcoxon $p$} \\\\\n\\midrule\nKASTLE-X + isotonic & $+0.0039$ & $[0.0028,\\ 0.0049]$ & $0.0001$ & $0.0625$ \\\\\nKASTLE-X KANres meta & $+0.0027$ & $[-0.0073,\\ 0.0127]$ & $0.5517$ & $1.0000$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $\\mathbf{+0.0114}$ & $\\mathbf{[0.0057,\\ 0.0172]}$ & $\\mathbf{0.0036}$ & $\\mathbf{0.0625}$ \\\\\nSoft voting & $+0.0045$ & $[0.0009,\\ 0.0082]$ & $0.0239$ & $0.0625$ \\\\\nRank-average voting & $+0.0061$ & $[-0.0035,\\ 0.0157]$ & $0.1619$ & $0.1875$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsubsection{Statistical Justification for the AUC Gain (Reviewer 3)}\n\nReviewer 3 raises the question of whether a $0.0114$ AUC gain is meaningful given only 237 positive observations. We address this at two levels. (1) \\emph{Statistical level}: the paired $t$-test detects a consistent within-fold improvement ($p=0.0036$) that is not attributable to sampling noise across folds; the 95\\% CI $[0.0057,\\ 0.0172]$ excludes zero. (2) \\emph{Practical level}: operationally, the F1 gain of $+0.0698$ translates directly to more correct attrition identifications per screening cycle. At the F1-optimal threshold, KASTLE-X correctly identifies 141 true positives compared with $\\approx 124$ for Stacking-LR (no KAN)---17 additional employees correctly flagged per full-workforce screening, reducing downstream replacement costs. We emphasize that these figures are illustrative for a synthetic benchmark and are not an organizational deployment study.\n\n\\subsection{Pooled Out-of-Fold Analysis}\n\nOn pooled OOF predictions (all 1{,}470 examples evaluated exactly once), KASTLE-X achieves AUC $=0.8404$, PR-AUC $=0.6432$, and at $\\tau^*=0.716$, F1 $=0.6091$. Confusion matrix: $[[1148,\\ 85],\\ [96,\\ 141]]$ (stayers/leavers predicted correctly on the diagonal). This yields sensitivity $=59.49\\%$, specificity $=93.11\\%$, precision $=62.39\\%$, false-positive rate $=6.89\\%$.\n\n\\textbf{Business translation (illustrative, synthetic benchmark).} A monthly screening of the full workforce would flag 226 employees (15.4\\%), of whom 141 are genuine attrition risks---a $3.7\\times$ enrichment over the 16.1\\% base attrition rate. At the F1-optimal threshold, the model would identify approximately 3 out of every 5 at-risk employees for proactive intervention. These figures are explicitly illustrative and should not be interpreted as deployment-ready estimates for any real organization, as the underlying dataset is synthetic.\n\n\\subsection{Meta-Learner Interpretability}\n\nThe logistic meta-learner coefficients trained on all 1{,}470 pooled OOF predictions provide a direct measure of each base learner's marginal contribution to the ensemble (Table~\\ref{tab:meta}). KAN-Bag receives the largest positive coefficient ($+2.5052$), followed by random forest ($+1.3778$) and logistic regression ($+1.1095$). The negative coefficients for LightGBM and HistGB reflect redundancy with other pool members, not individual harmfulness. The pool's prediction correlation matrix confirms KAN-Bag has the lowest average pairwise correlation with remaining pool members (Figure~\\ref{fig:pooldiv}), validating the architectural diversity argument.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Meta-learner coefficients from the logistic regression trained on all 1{,}470 pooled OOF predictions. A positive coefficient indicates a net positive marginal contribution; negative coefficients reflect redundancy with higher-weighted pool members.}\\label{tab:meta}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Base Learner} & \\textbf{Meta Coefficient} & \\textbf{Interpretation} \\\\\n\\midrule\nKAN-Bag & $+2.5052$ & Largest marginal contribution; architecturally distinct \\\\\nRandom Forest & $+1.3778$ & Strong independent variance reduction \\\\\nLogistic Regression & $+1.1095$ & Orthogonal linear signal \\\\\nCatBoost & $+0.7608$ & Distinct ordered-boosting signal \\\\\nXGBoost & $+0.5165$ & Moderate incremental value \\\\\nExtra Trees & $+0.2423$ & Small but positive incremental gain \\\\\nHistGB & $-0.1212$ & Redundant with LightGBM/XGBoost \\\\\nLightGBM & $-0.3363$ & Redundant with XGBoost/HistGB \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_67.png}\n\\end{center}\n\\caption{Pool prediction-correlation matrix. KAN-Bag has the lowest average pairwise correlation with remaining pool members, supporting the architectural diversity argument.}\\label{fig:pooldiv}\n\\end{figure}\n\n\\subsection{SHAP Interpretability}\\label{sec:shap}\n\nTreeSHAP was applied to the Optuna-tuned LightGBM learner (Figures~\\ref{fig:beeswarm} and~\\ref{fig:shapimp}). We note explicitly (per Reviewer 2) that this SHAP analysis explains the LightGBM \\emph{component} of KASTLE-X, not the full ensemble; it is positioned as component-level evidence for feature importance rather than ensemble-level attribution. The meta-learner coefficients (Table~\\ref{tab:meta}) and the prediction-diversity matrix (Figure~\\ref{fig:pooldiv}) provide the ensemble-level view.\n\nThe five most influential features are \\textsc{OverTime\\_Yes}, \\textsc{OverTimeStress} ($f_{10}$, engineered), \\textsc{MonthlyIncome}, \\textsc{IncomePerLevel} ($f_1$, engineered), and \\textsc{TotalWorkingYears}. Overtime exerts the largest single effect. The engineered $f_{10}$ provides complementary dose--response information beyond the binary indicator. Income features show a strong monotone negative relationship with attrition. These patterns are consistent across income, role, and tenure dimensions (Figures~\\ref{fig:dep_income}--\\ref{fig:dep_joblevel}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_66.png}\n\\end{center}\n\\caption{SHAP beeswarm summary for the tuned LightGBM component (not the full KASTLE-X ensemble). This analysis provides component-level feature attribution.}\\label{fig:beeswarm}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_65.png}\n\\end{center}\n\\caption{Mean absolute SHAP feature importance for the tuned LightGBM component.}\\label{fig:shapimp}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_61.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{MonthlyIncome}, coloured by overtime status.}\\label{fig:dep_income}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_63.png}\n\\end{center}\n\\caption{SHAP dependence plot for engineered \\textsc{IncomePerLevel} ($f_1$).}\\label{fig:dep_ipl}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_62.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{YearsAtCompany}, showing front-loaded early-tenure attrition risk.}\\label{fig:dep_years}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_64.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{JobLevel}, showing monotone decrease in attrition contribution with seniority.}\\label{fig:dep_joblevel}\n\\end{figure}\n\n\n%===================================================================\n\\section{Discussion}\\label{sec:discussion}\n%===================================================================\n\n\\subsection{Theoretical Significance}\n\nThis study contributes to two theoretical streams. First, it provides direct empirical evidence that KANs---whose learnable polynomial edge functions can represent monotone and non-monotone response curves flexibly---are architecturally distinctive from GBDTs on small-scale, noisy HR tabular data. Specifically, KAN-Bag achieves higher AUC than all four GBDT variants at the zoo benchmark stage, a result consistent with the hypothesis that the attitudinal Likert features in this dataset have response relationships better captured by polynomial bases than by axis-aligned splits. Second, the KAN-augmented stacking result confirms ensemble diversity theory \\citep{kuncheva_whitaker}: when a new learner's error correlations with an existing pool are lower than the pool's internal correlations, adding it improves the ensemble even when its standalone AUC is not highest, because the meta-learner can exploit its residual information.\n\n\\subsection{Empirical Contributions}\n\nThis study provides the most complete honest evaluation of the IBM HR attrition benchmark to date: 20 individual models, 6 ensemble variants, 7 performance metrics, formal statistical tests with confidence intervals, calibration analysis, and component ablation, all under a protocol that eliminates leakage. The comparison with published prior work on the same dataset, summarized in Table~\\ref{tab:prior}, illustrates the evaluation-protocol dependence of reported performance: studies using pre-split SMOTE report F1 values 25--50 percentage points above our honest estimates, confirming the data-leakage hypothesis of \\citet{rahman_review}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Comparison with published results on the IBM HR Analytics benchmark. Studies are ordered by reported AUC. All our results are from the current honest nested-CV evaluation. The protocol column flags the primary methodological concern.}\\label{tab:prior}\n\\footnotesize\n\\begin{tabular}{lcccp{4.2cm}}\n\\toprule\n\\textbf{Study} & \\textbf{Best Model} & \\textbf{Reported AUC} & \\textbf{Reported F1} & \\textbf{Evaluation Protocol} \\\\\n\\midrule\n\\citet{bibliometric_attrition_2025} & Ensemble & $\\sim$0.90 & $\\sim$0.88 & Pre-split SMOTE (leakage likely) \\\\\n\\citet{slr_attrition_2024} & XGBoost & $\\sim$0.87 & $\\sim$0.83 & Hold-out; pre-split oversampling \\\\\n\\citet{alqarni_power_bi_2025} & RF + BI & $\\sim$0.86 & $\\sim$0.81 & Single split; pre-split SMOTE \\\\\n\\textbf{This study} (KASTLE-X) & Stacking & $0.8449$ & $0.5831$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\textbf{This study} (KAN-Bag) & Individual & $0.8485$ & $0.5945$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Practical Implications}\n\nFor HR analytics practitioners, the results have several actionable implications. First, the $3.7\\times$ enrichment of the KASTLE-X screening list over the base attrition rate means that a limited number of HR interventions can be directed at the highest-risk employees, substantially improving the cost-effectiveness of retention programs. Second, the SHAP analysis identifies overtime load, income adequacy, and early tenure as the three primary attrition drivers in this benchmark; targeted interventions addressing these factors (flexible work arrangements, transparent compensation benchmarking, structured onboarding programs) may be more effective than generic engagement programs. Third, practitioners should select the decision threshold $\\tau^*$ based on the asymmetric costs of false positives (unnecessary retention spending) and false negatives (missed departures) in their organizational context, rather than using the default 0.5. Fourth, we emphasize that KASTLE-X is a predictive association model, not a causal intervention model: finding that overtime predicts attrition does not by itself prove that reducing overtime would reduce attrition, and causal claims require randomized field experiments.\n\n\\subsection{Research Limitations}\n\n\\textbf{Single-dataset scope.} The study uses one benchmark dataset representing one organization in a synthetic release. All performance figures are bounds on this specific benchmark; generalization to other organizational contexts, industries, or cultures requires external validation. In the absence of a second public HR attrition dataset with equivalent attributes, we clearly position this as a single-dataset limitation central to the conclusion.\n\n\\textbf{Statistical power.} Five outer folds limits the Wilcoxon test to its minimum $p=0.0625$. The paired $t$-test provides more power under the normality assumption but is sensitive to that assumption with $n=5$. Replication with ten-fold outer CV would provide more reliable inferences.\n\n\\textbf{Dataset size.} With 237 positive cases, the standard error on minority-class metrics is substantial. The component ablation results and fold-wise AUC differences are consistent but should be interpreted with this in mind.\n\n\\textbf{SHAP scope.} The SHAP analysis explains the LightGBM component, not the full ensemble. Full-ensemble attributions would require model-agnostic methods (e.g., LIME or Kernel SHAP) applied to the meta-learner output, which is a direction for future work.\n\n\\textbf{Causal interpretation.} Predictive associations identified by SHAP do not imply causal effects. The claim that overtime load predicts attrition is a predictive association, not evidence that reducing overtime would reduce attrition.\n\n\\subsection{Ethical Considerations and Responsible Deployment}\n\nAutomated attrition prediction tools carry several ethical risks that practitioners must address before deployment. First, even a well-calibrated model will produce false positives---employees flagged as at-risk who are not. If such flags influence managerial behavior (differential treatment, reduced promotion consideration), they may create self-fulfilling prophecies or constitute indirect discrimination. Second, the SHAP analysis shows that age and income are among the top predictors; if these are correlated with protected characteristics in a particular organization, the model may produce disparate-impact screening. Third, employees should be informed that such tools are in use and should have recourse to challenge model-generated assessments.\n\nSHAP-based explainability, as demonstrated in this paper, is a necessary but not sufficient mitigation: it enables identification of which features drive predictions, but does not verify that the model is fair across demographic subgroups, and does not substitute for organizational governance. We recommend that any deployment of systems like KASTLE-X include: (a) a fairness audit across age, gender, and ethnicity subgroups; (b) transparency with affected employees; (c) human oversight for any consequential decisions; and (d) regular re-evaluation as workforce composition and organizational context change.\n\n\\subsection{Future Research Directions}\n\n\\textbf{External validation.} The most important next step is evaluating KASTLE-X on additional organizational attrition datasets. We are not aware of a second public dataset with equivalent attribute richness for direct comparison; constructing or obtaining such a dataset is a valuable research contribution in itself.\n\n\\textbf{Full-ensemble interpretability.} Developing model-agnostic ensemble SHAP attributions that reflect the combined meta-learner output would align interpretability with the model actually deployed.\n\n\\textbf{Larger KAN pools.} As KAN research matures and computational costs decrease, adding multiple KAN variants (wavelet KAN, B-spline KAN) to the stacking pool may further increase diversity.\n\n\\textbf{Longitudinal validation.} A prospective validation study in which model-flagged employees are tracked over time would allow calibration of confidence intervals on the business-impact figures and provide causal evidence if combined with randomized retention interventions.\n\n\\textbf{Fairness-aware variants.} Adapting KASTLE-X with fairness constraints \\citep{lundberg_shap} on demographic parity or equalized odds would extend its applicability to contexts with stringent anti-discrimination requirements.\n\n\n%===================================================================\n\\section{Conclusion}\\label{sec:conclusion}\n%===================================================================\n\nThis paper presented KASTLE-X, a KAN-augmented stacking ensemble for employee attrition prediction. The primary contribution is a rigorous test of the hypothesis that an architecturally distinct KAN component---specifically KAN-Bag, a seed-bagged Chebyshev-polynomial KAN---provides incremental value within a heterogeneous stacking ensemble. The answer, clearly bounded to this single synthetic benchmark, is yes: KASTLE-X outperforms the identically structured non-KAN stacking ensemble on all five outer folds ($p=0.0036$; $\\Delta$AUC $=+0.0114$, 95\\% CI $[0.0057,\\ 0.0172]$; $\\Delta$F1 $=+0.0698$). The logistic meta-learner assigns KAN-Bag the largest coefficient ($2.51$), and the prediction-diversity analysis confirms that KAN-Bag's error correlations with the GBDT cluster are substantially lower than intra-GBDT correlations.\n\nThe narrower claim---that KAN augmentation within stacking \\emph{may} benefit tabular ensembles under class imbalance---is better grounded and more scientifically defensible than any claim of universal superiority. KAN-Bag is also the strongest of 20 individually benchmarked classifiers (AUC $0.8485$), outperforming CatBoost, XGBoost, LDA, and all other individual models. Twelve leakage-free engineered features confirmed by mutual-information analysis and SHAP interpretability (at the component level) add measurable informativeness. A component ablation isolates the contributions of feature engineering ($+0.030$ AUC), seed bagging ($+0.016$), and Bayesian optimization ($+0.009$).\n\nThe broader methodological contribution is the most complete honest evaluation of the IBM HR attrition benchmark to date, covering 20 models, 6 ensemble variants, 7 metrics, component ablation, calibration, statistical tests with confidence intervals, and SHAP interpretability under a strictly leakage-free nested protocol. These results advance both the practical toolkit for HR analytics and the nascent empirical literature on KAN applications to business tabular data.\n\n\n%===================================================================\n\\section*{Conflict of Interest Statement}\n%===================================================================\nThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n\\section*{Author Contributions}\nFA conceived the study, designed the KASTLE-X framework and KAN-Bag classifier, implemented the experimental pipeline, and drafted the manuscript. SA contributed to feature engineering design, statistical analysis, and manuscript revision. TA supervised the study, contributed to interpretation and SHAP analysis, and revised the manuscript. All authors read and approved the final manuscript.\n\n\\section*{Funding}\nThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\n\n\\section*{Acknowledgments}\nThe authors thank the maintainers of the open-source scientific Python ecosystem (scikit-learn, LightGBM, XGBoost, CatBoost, PyTorch, Optuna) and the three anonymous reviewers whose detailed critiques substantially improved the manuscript.\n\n\\section*{Supplemental Data}\n\\href{http://home.frontiersin.org/about/author-guidelines#SupplementaryMaterial}{Supplementary Material} accompanying this article contains: (S1) complete Python implementation of the KASTLE-X pipeline; (S2) per-fold hyperparameter selections for LightGBM and XGBoost; (S3) fixed hyperparameter configurations for all other pool members; (S4) additional interpretability figures; (S5) full numerical results for all 20 individual classifiers and 6 ensemble variants.\n\n\\section*{Data Availability Statement}\nThe IBM HR Analytics Employee Attrition \\& Performance dataset is publicly available at \\url{https://www.kaggle.com/datasets/pavansubhasht/ibm-hr-analytics-attrition-dataset}. All code required to reproduce the reported results is provided as supplementary material.\n\n\\bibliographystyle{Frontiers-Harvard}\n\\bibliography{test_revised}\n\n\\end{document}",
      "tex_filename": "frontiers.tex",
      "bib_content": "@article{Paul2026,\n  title={KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction},\n  author={Nirodh Paul and Md. Mahedi Hassan and Sumnoon Ferdous and Md. Masuqul Haque and Mir Mohammad Azad},\n  journal={Frontiers in Education},\n  doi={10.3389/feduc.2026.1230645},\n  year={2026}\n}\n",
      "source_dir": "/journals/education/articles/10.3389/feduc.2026.8922077/source",
      "tex_file": "/journals/education/articles/10.3389/feduc.2026.8922077/source/article.tex",
      "bib_file": "/journals/education/articles/10.3389/feduc.2026.8922077/source/references.bib",
      "updated_at": "2026-11-07T23:37:36Z",
      "created_at": "2026-11-07T11:14:03Z"
    },
    {
      "title": "KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction",
      "authors": [
        {
          "name": "Nirodh Paul",
          "affiliations": [
            "1"
          ],
          "is_corresponding": false,
          "affil_str": "1",
          "initials": "NP"
        },
        {
          "name": "Md. Mahedi Hassan",
          "affiliations": [
            "2"
          ],
          "is_corresponding": false,
          "affil_str": "2",
          "initials": "MH"
        },
        {
          "name": "Sumnoon Ferdous",
          "affiliations": [
            "3"
          ],
          "is_corresponding": false,
          "affil_str": "3",
          "initials": "SF"
        },
        {
          "name": "Md. Masuqul Haque",
          "affiliations": [
            "4"
          ],
          "is_corresponding": false,
          "affil_str": "4",
          "initials": "MH"
        },
        {
          "name": "Mir Mohammad Azad",
          "affiliations": [
            "5"
          ],
          "is_corresponding": false,
          "affil_str": "5",
          "initials": "MA"
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh"
        },
        {
          "index": "2",
          "text": "Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh"
        },
        {
          "index": "3",
          "text": "Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh"
        },
        {
          "index": "4",
          "text": "Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh"
        },
        {
          "index": "5",
          "text": "Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh"
        }
      ],
      "corr_author": "",
      "corr_email": "kotpiuznd141@hotmail.com",
      "abstract": "Employee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov\u2013Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds incremental value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12% positive prevalence) under a nested 5{\u00d7}5-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC (0.8485 \u00b1 0.0266) and F1 (0.5945). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by +0.0114 (p = 0.0036, paired t-test; Wilcoxon minimum p = 0.0625, n=5 folds), PR-AUC by +0.0188, and F1 by +0.0698 on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the 0.0114 AUC gain\u2014achieved with only 237 positive cases\u2014against its practical screening benefit (3.7\u00d7 enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov\u2013Arnold networks provide distinct diversity that may benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.",
      "keywords": "employee attrition; Kolmogorov\u2013Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning",
      "doi": "10.3389/frai.2026.3861612",
      "article_url_path": "/journals/artificial-intelligence/articles/10.3389/frai.2026.3861612/abstract",
      "journal_slug": "artificial-intelligence",
      "journal": "Frontiers in Artificial Intelligence",
      "journal_abbrev": "Front. Artif. Intell.",
      "section": "Sec. Medicine and Public Health",
      "banner": "/assets/images/journals/artificial-intelligence-banner.png",
      "issn": "2624-8212",
      "impact_factor": "6.7",
      "citescore": "8",
      "received": "2026-10-20",
      "accepted": "2026-11-01",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
      "views_count": "1098",
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          "name": "United States",
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          "name": "Bangladesh",
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        },
        {
          "name": "India",
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        },
        {
          "name": "Morocco",
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      ],
      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Revised manuscript: KASTLE-X \u2014 Major Revision addressing Reviewers 1, 2, and 3\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%% Version 3.4 Generated 2022/06/14 %%%\n\\documentclass[utf8]{FrontiersinHarvard}\n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\\usepackage{amsmath,amssymb,booktabs,array,xcolor}\n\n\\linenumbers\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\\def\\firstAuthorLast{Author {et~al.}}\n\\def\\Authors{Nirodh Paul\\,$^{1}$, Md. Mahedi Hassan\\,$^{2}$, Sumnoon Ferdous\\,$^{3}$, Md. Masuqul Haque\\,$^{4}$ and Mir Mohammad Azad\\,$^{5}$}\n\\def\\Address{$^{1}$Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh \\\\\n$^{2}$Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh \\\\\n$^{3}$Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh \\\\\n$^{4}$Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh \\\\\n$^{5}$Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh}\n\n\\def\\corrAuthor{}\n\\def\\corrEmail{kotpiuznd141@hotmail.com}\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title[KASTLE-X for Employee Attrition Prediction]{KASTLE-X: Incremental Value of Kolmogorov--Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction}\n\n\\author[\\firstAuthorLast]{\\Authors}\n\\address{}\n\\correspondance{}\n\\extraAuth{}\n\n\\maketitle\n\n%-------------------------------------------------------------------\n\\begin{abstract}\n\\section{}\n\nEmployee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov--Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds \\emph{incremental} value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12\\% positive prevalence) under a nested $5{\\times}5$-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC ($0.8485 \\pm 0.0266$) and F1 ($0.5945$). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by $+0.0114$ ($p = 0.0036$, paired $t$-test; Wilcoxon minimum $p = 0.0625$, $n=5$ folds), PR-AUC by $+0.0188$, and F1 by $+0.0698$ on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the $0.0114$ AUC gain---achieved with only 237 positive cases---against its practical screening benefit ($3.7\\times$ enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov--Arnold networks provide distinct diversity that \\emph{may} benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.\n\n\\tiny\n \\keyFont{ \\section{Keywords:} employee attrition; Kolmogorov--Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning}\n\\end{abstract}\n\n\n%===================================================================\n\\section{Introduction}\n%===================================================================\n\n\\subsection{Research Context and Practical Motivation}\n\nVoluntary employee turnover is among the costliest operational events an organization can experience. Replacement expenditures are estimated at 50\\%--200\\% of a departing employee's annual salary \\citep{shrm_replacement_cost}, encompassing direct recruitment and onboarding costs as well as indirect costs from lost institutional knowledge and disrupted team cohesion. In large organizations, aggregate replacement costs readily reach tens of millions of dollars annually. Predictive analytics applied to routine HR records therefore represents a high-value operational intervention: identifying employees with elevated attrition risk in advance enables targeted engagement programs, compensation adjustments, or career-development conversations at a fraction of the replacement cost.\n\n\\subsection{Technical Challenges}\n\nThe machine-learning framing of attrition prediction is a binary classification task on a small, heterogeneous, highly imbalanced tabular dataset. Three structural properties make it genuinely challenging. First, the positive class is scarce: in the widely used IBM HR Analytics benchmark, only 237 of 1{,}470 employees (16.12\\%) left \\citep{ibm_dataset}. Second, the feature space mixes ordinal Likert scales, categorical job descriptors, and continuous financial variables whose marginal predictive power is modest after accounting for correlations. Third, the label contains substantial irreducible noise from personal events invisible in HR records, setting a genuine Bayes error floor. These properties cap achievable F1 at values that may seem moderate in absolute terms but represent genuine predictive value relative to the no-skill baseline.\n\n\\subsection{Methodological Gap}\n\nThe literature on attrition prediction is characterized by two concurrent weaknesses. First, published evaluations frequently report inflated performance because synthetic minority oversampling \\citep{chawla_smote} is applied before the train--test split, allowing synthetic copies of minority test samples to appear in training data \\citep{rahman_review}. Second, no published study has systematically examined whether Kolmogorov--Arnold Networks (KANs) \\citep{liu_kan}---a recently proposed architecture with learnable polynomial edge functions---add useful architectural diversity to stacking ensembles of conventional tabular learners. Architectural diversity is the primary mechanism through which stacking exceeds its constituent base learners \\citep{kuncheva_whitaker}, and dominant gradient-boosted decision tree (GBDT) variants in current pools often have prediction correlations exceeding 0.9, leaving limited room for meta-learner exploitation.\n\n\\subsection{Research Objectives}\n\nThis study addresses four objectives:\n\\begin{enumerate}\n  \\item[\\textbf{O1}] Establish a leakage-free benchmark of 20 individual classifiers spanning all major tabular algorithmic families on the engineered IBM HR dataset.\n  \\item[\\textbf{O2}] Develop KAN-Bag, a seed-bagged Chebyshev-polynomial KAN classifier, and quantify the separate contributions of the KAN architecture, seed bagging, and feature engineering through ablation.\n  \\item[\\textbf{O3}] Evaluate whether KAN-Bag provides statistically meaningful incremental value when added to a heterogeneous stacking ensemble (KASTLE-X vs.\\ Stacking-LR without KAN).\n  \\item[\\textbf{O4}] Characterize the practical limitations of the findings, including the single-dataset scope, small sample size, and implications for responsible HR deployment.\n\\end{enumerate}\n\n\\subsection{Contributions}\n\nAgainst these objectives, the specific contributions are: (i) \\emph{KAN-Bag}: a seed-bagged Chebyshev-polynomial KAN tabular classifier that achieves the highest individual AUC among 20 compared classifiers; (ii) \\emph{KASTLE-X}: a KAN-augmented stacking ensemble with a class-weighted logistic meta-learner, demonstrated to improve over the non-KAN stacking baseline on all five outer folds ($p=0.0036$); (iii) twelve leakage-free, domain-motivated engineered features confirmed by mutual-information analysis; (iv) a component ablation isolating the contributions of KAN architecture, seed bagging, and feature engineering; and (v) the most comprehensive honest evaluation of the IBM HR attrition benchmark to date, covering 20 individual models, 6 ensemble variants, 7 performance metrics, calibration analysis, statistical tests with explicitly bounded claims, and SHAP interpretability.\n\nThe remainder of the paper is organized as follows. Section~\\ref{sec:related} reviews related work. Section~\\ref{sec:methods} presents the dataset, exploratory analysis, feature engineering, KAN architecture, KASTLE-X framework, hyperparameter optimization, and evaluation protocol. Section~\\ref{sec:results} presents experimental results. Section~\\ref{sec:discussion} discusses findings, limitations, ethical considerations, and future directions. Section~\\ref{sec:conclusion} concludes.\n\n%===================================================================\n\\section{Literature Review}\\label{sec:related}\n%===================================================================\n\n\\subsection{Employee Attrition Prediction}\n\nEarly computational approaches to employee turnover used logistic regression and survival analysis. The democratization of the IBM HR Analytics dataset catalyzed a shift toward ML experimentation, with subsequent studies applying support vector machines, decision trees, random forests, gradient-boosting machines, and neural networks. \\citet{rahman_review} found that gradient-boosted ensembles---particularly XGBoost \\citep{chen_xgboost} and LightGBM \\citep{ke_lightgbm}---consistently produced the highest cross-validated AUC values (typically 0.80--0.87) when evaluation protocols were correctly specified.\n\nA pervasive concern is data leakage through synthetic oversampling. When SMOTE \\citep{chawla_smote} is applied before the train--test split, synthetic copies of test-set minority instances appear in training data, producing optimistic estimates. Under honest within-fold resampling on the IBM benchmark, F1 values of 0.45--0.55 are typical; published values of 0.80--0.90 in studies using pre-split SMOTE are leakage artifacts. The present study applies no resampling and restricts all processing to training partitions.\n\nMore recent work has explored deep learning for tabular attrition prediction. TabNet \\citep{arik_tabnet} uses sequential attention to select relevant features at each step. However, benchmarks such as \\citet{grinsztajn_trees} consistently find that well-tuned GBDTs match or outperform neural tabular architectures on small-to-medium datasets, a finding attributable to the inductive biases of tree ensembles: robustness to irrelevant features, implicit feature selection, and resistance to overparameterization. Explainability has emerged as a central concern in HR analytics; SHAP \\citep{lundberg_shap} provides consistent, locally additive feature attributions with game-theoretic foundations.\n\nRecent literature has also begun examining the impact of class-imbalance strategies in HR classification. \\citet{alqarni_power_bi_2025} demonstrated that ML models with power BI dashboards for attrition can aid managerial decision-making, and \\citet{bibliometric_attrition_2025} provided a bibliometric synthesis of ML methods for employee attrition prediction, identifying gradient boosting and neural networks as the most frequently applied approaches. \\citet{slr_attrition_2024} conducted a systematic literature review of quantitative attrition models, confirming that ensemble methods dominate recent publications but that rigorous leakage-free protocols remain underrepresented.\n\n\\subsection{Ensemble Learning and Stacking}\n\nBagging reduces variance by averaging predictions over bootstrap subsamples; boosting reduces bias through additive residual fitting; stacking \\citep{wolpert_stacking} trains a meta-learner on out-of-fold predictions from heterogeneous base learners. The meta-learner learns the optimal combination rather than assuming a fixed rule.\n\nDiversity of base learners is central to stacking's benefit: if all base learners make correlated errors, the meta-learner has no information to correct them. \\citet{kuncheva_whitaker} formalized this diversity--accuracy trade-off, showing that ensembles benefit most when base-learner errors are conditionally independent. Practical stacking implementations achieve diversity by combining learners with different inductive biases---linear models, kernel machines, tree ensembles, and neural architectures. However, GBDT variants dominate current tabular stacking pools, and their prediction correlations often exceed 0.9. Super-learner theory \\citep{vanderlaan_superlearner} provides asymptotic justification: under regularity conditions, the cross-validated stacked ensemble converges to the oracle model minimizing expected loss among all convex combinations of base learners.\n\n\\subsection{Kolmogorov--Arnold Networks and Tabular Deep Learning}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957, arnold_1963} establishes that any continuous $f:[0,1]^n\\to\\mathbb{R}$ can be written as a finite composition of continuous univariate functions and additions. \\citet{liu_kan} proposed KANs as a neural architecture inspired by this theorem, replacing fixed activations on nodes with learnable univariate functions on edges parameterized by B-splines. Subsequent work has explored alternative bases: \\citet{bozorgasl_wavkan} used wavelets; Chebyshev polynomial bases offer computational advantages through a stable three-term recurrence.\n\nThe current empirical state of KAN research for tabular classification reveals a nuanced picture. Early evidence from \\citet{liu_kan} demonstrated that KANs can match or exceed MLPs on scientific and regression tasks with fewer parameters. However, the broader tabular deep-learning literature---as surveyed in \\citet{grinsztajn_trees} and synthesized in \\citet{arik_tabnet}---consistently finds that GBDTs retain an advantage on small-to-medium tabular datasets due to their ability to handle irregular feature distributions, categorical variables, and uninformative features without specialized architectural inductive biases. KANs, like MLPs, lack these inductive biases, making their advantage domain-dependent. On small, imbalanced HR datasets---the focus of this paper---their behavior as standalone predictors and as ensemble components has received little systematic attention. This study contributes such an assessment.\n\n\n%===================================================================\n\\section{Materials and Methods}\\label{sec:methods}\n%===================================================================\n\n\\noindent\\textbf{Glossary.}\n\\begin{center}\n\\begin{tabular}{lp{0.72\\linewidth}}\n\\toprule\n\\textbf{Term} & \\textbf{Definition} \\\\\n\\midrule\nLeakage-free feature engineering & Features constructed as row-wise transformations that depend only on the individual observation and universal constants, with no reference to other rows, group statistics, or the target variable. \\\\\nNested cross-validation & A two-level CV protocol in which the outer loop evaluates model performance and the inner loop handles all model selection and tuning, ensuring outer test folds are never touched during optimization. \\\\\nMeta-learner & The second-level model in a stacking ensemble that is trained on the out-of-fold predictions of base learners and learns the optimal combination of their outputs. \\\\\nOOF (out-of-fold) predictions & Predictions on held-out inner validation folds; every training example receives a prediction from a model that was never fitted on it. \\\\\nKAN-Bag & The seed-bagged Chebyshev-polynomial KAN classifier proposed in this study. \\\\\nKASTLE-X & The full stacking ensemble combining KAN-Bag with seven conventional Bayesian-optimized learners. \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\n\\subsection{Dataset and Preprocessing}\n\nThe IBM HR Analytics Employee Attrition \\& Performance dataset \\citep{ibm_dataset} contains 1{,}470 employee records with 35 attributes. The binary target \\textsc{Attrition} takes value \\textit{Yes} for 237 records (16.12\\%) and \\textit{No} for 1{,}233 records (83.88\\%), yielding an imbalance ratio of approximately $5.2{:}1$. The dataset has zero missing values and zero duplicated rows. Four non-informative constant columns (\\textsc{EmployeeCount}, \\textsc{Over18}, \\textsc{StandardHours}, \\textsc{EmployeeNumber}) were removed, leaving 30 raw attributes spanning five conceptual domains: (a) demographics, (b) compensation and incentives, (c) job context, (d) attitudinal Likert scales, and (e) tenure history. Seven categorical features were one-hot encoded without reference-category dropping, producing a 51-feature matrix from raw attributes. Models requiring standardized inputs (logistic regression, SVM, KAN) applied a \\textsc{StandardScaler} fitted exclusively on the training partition of each fold.\n\n\\textbf{Important contextual note.} The IBM HR Analytics dataset is a synthetic release used widely as a benchmark. The present study treats it as such: all findings are bounds on a single synthetic benchmark, and generalization to other organizations requires external validation.\n\n\\subsection{Leakage-Free Feature Engineering}\n\nTwelve domain-motivated engineered features were constructed as strictly row-wise transformations, using only the individual row's attributes and universal constants. This makes data leakage structurally impossible: the same mapping applies to any training or test partition. Let $\\text{OT}=\\mathbb{1}\\{\\textsc{OverTime}=\\textit{Yes}\\}$ and $\\varepsilon=10^{-6}$. Intuitively, these features encode quantities that standard employee records capture indirectly: for instance, $f_1$ measures income adequacy relative to job level (detecting undercompensation), $f_5$ measures career stagnation, and $f_{10}$ captures the interaction of overtime demand with work--life balance (an overtime stress signal). Such constructions reflect the job-demands--resources model from organizational psychology.\n\n\\begin{align}\nf_1 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{JobLevel}+\\varepsilon}, &\nf_2 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{Age}+\\varepsilon}, &\nf_3 &= \\frac{\\textsc{YearsAtCompany}}{\\textsc{TotalWorkingYears}+1} \\label{eq:fe1}\\\\\nf_4 &= \\frac{\\textsc{TotalWorkingYears}}{\\textsc{NumCompaniesWorked}+1}, &\nf_5 &= \\frac{\\textsc{YearsSinceLastPromotion}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe2}\\\\\nf_6 &= \\frac{\\textsc{YearsWithCurrManager}}{\\textsc{YearsAtCompany}+1}, &\nf_7 &= \\frac{\\textsc{YearsInCurrentRole}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe3}\\\\\nf_8 &= \\tfrac{1}{4}(\\textsc{JobSat}+\\textsc{EnvSat}+\\textsc{RelSat}+\\textsc{WLB}), &\nf_9 &= \\textsc{JobInvolvement}\\times\\textsc{JobSatisfaction} \\label{eq:fe4}\\\\\nf_{10} &= \\text{OT}\\times(5-\\textsc{WLB}), &\nf_{11} &= \\textsc{DistanceFromHome}\\times\\text{OT}, &\nf_{12} &= \\frac{\\textsc{PercentSalaryHike}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe5}\n\\end{align}\n\nTogether with the 51 raw encoded features, the final design matrix is $\\mathbf{X}\\in\\mathbb{R}^{1470\\times 63}$.\n\n\\subsection{Component Contribution Ablation}\n\nTo isolate the contributions of the KAN architecture, seed bagging, Bayesian optimization, and feature engineering---as requested by Reviewer 3---we conducted a four-condition ablation on a fixed 5-fold stratified CV (Table~\\ref{tab:ablation_components}). Condition A uses raw (non-engineered) features, a single-seed KAN-Net without bagging, and no Bayesian optimization. Each subsequent condition adds one component. This design supports attributing performance increments to specific methodological choices rather than to the composite package.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Component contribution ablation ($5$-fold stratified CV, mean $\\pm$ std on AUC). Each row adds one component to the prior row to isolate its contribution.}\\label{tab:ablation_components}\n\\begin{tabular}{llccc}\n\\toprule\n\\textbf{Condition} & \\textbf{Components Active} & \\textbf{AUC} & \\textbf{F1} & $\\boldsymbol{\\Delta}$ \\textbf{AUC vs.\\ A} \\\\\n\\midrule\nA & Raw features, single-seed KAN-Net & $0.7931 \\pm 0.031$ & $0.4853$ & --- \\\\\nB & + Engineered features ($f_1$--$f_{12}$) & $0.8227 \\pm 0.016$ & $0.5426$ & $+0.0296$ \\\\\nC & + Seed bagging ($S=3$, no BO) & $0.8391 \\pm 0.022$ & $0.5712$ & $+0.0460$ \\\\\nD & + Bayesian hyperparameter optimization & $0.8485 \\pm 0.027$ & $0.5945$ & $+0.0554$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nThe ablation shows that feature engineering contributes $+0.030$ AUC, seed bagging a further $+0.016$, and Bayesian optimization a further $+0.009$. These increments are additive and independently meaningful. The KAN architecture itself is best assessed by comparing Condition A against the analogous MLP-based condition (Table~\\ref{tab:zoo}), where KAN-Net (single seed) outperforms the MLP by $0.0394$ AUC on the same engineered features.\n\n\\subsection{Chebyshev-KAN Tabular Classifier}\n\n\\subsubsection{Architecture}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957} states that any continuous $f:[0,1]^n\\to\\mathbb{R}$ admits\n\\begin{equation}\\label{eq:ka_theorem}\nf(x_1,\\ldots,x_n) = \\sum_{q=0}^{2n} \\Phi_q\\!\\left(\\sum_{p=1}^{n}\\varphi_{q,p}(x_p)\\right)\n\\end{equation}\nfor continuous univariate functions $\\varphi_{q,p}$ and $\\Phi_q$. Intuitively, this guarantees that the network can, in principle, represent complex nonlinear interactions between employee features and attrition risk without requiring an exponentially growing number of parameters.\n\nMotivated by~\\eqref{eq:ka_theorem}, an $L$-layer KAN with width vector $[n_0,\\ldots,n_L]$ applies at each layer $\\ell$ a learnable univariate edge function $\\varphi_{\\ell,j,i}$ to each input coordinate $x_{\\ell,i}$ and sums:\n\\begin{equation}\\label{eq:kan_layer}\nx_{\\ell+1,j} = \\sum_{i=1}^{n_\\ell} \\varphi_{\\ell,j,i}(x_{\\ell,i}), \\quad j=1,\\ldots,n_{\\ell+1}.\n\\end{equation}\n\nWe parameterize each edge function using a Chebyshev polynomial basis of degree $D$. The Chebyshev polynomials $T_0,T_1,\\ldots,T_D$ satisfy the three-term recurrence\n\\begin{equation}\\label{eq:cheby_rec}\nT_0(u)=1,\\quad T_1(u)=u,\\quad T_k(u) = 2u\\,T_{k-1}(u) - T_{k-2}(u),\n\\end{equation}\nwhich admits stable batched computation. To ensure inputs lie in $[-1,1]$ (the polynomial's natural domain), a $\\tanh$ squashing is applied before basis expansion. Intuitively, this allows the network to model monotone and non-monotone response curves (e.g., the U-shaped relationship between tenure and attrition risk) through a small number of low-degree coefficients, which standard ReLU networks would require many hidden units to approximate.\n\nA ChebyKAN layer with input dimension $d_\\text{in}$, output dimension $d_\\text{out}$, and degree $D$ maintains a coefficient tensor $\\mathbf{C}\\in\\mathbb{R}^{d_\\text{in}\\times d_\\text{out}\\times(D+1)}$:\n\\begin{equation}\\label{eq:chebykan}\n\\text{out}_{j} = \\sum_{i=1}^{d_\\text{in}} \\sum_{k=0}^{D} \\mathbf{C}_{i,j,k}\\, T_k\\!\\big(\\tanh(x_i)\\big),\n\\end{equation}\nimplemented as a single \\textsc{einsum} contraction. The KAN-Net classifier is a two-layer ChebyKAN network:\n\\begin{equation}\\label{eq:kannet}\n\\mathbf{h} = \\text{LayerNorm}\\big(\\text{ChebyKAN}_{63\\to 24,D=3}(\\mathbf{x})\\big), \\quad \\hat{y} = \\sigma\\big(\\text{ChebyKAN}_{24\\to 1,D=3}(\\mathbf{h})\\big),\n\\end{equation}\nwith total parameter count $63\\cdot 24\\cdot 4 + 24\\cdot 1\\cdot 4 = 6{,}240$ trainable weights (excluding layer-norm), roughly half the comparable MLP ($64\\to 32\\to 1$, $\\approx 11{,}300$ parameters).\n\n\\subsubsection{Training Objective}\n\nGiven $N$ training examples with labels $y_i\\in\\{0,1\\}$ and class-imbalance ratio $r=N_-/N_+$, we minimize the class-weighted binary cross-entropy:\n\\begin{equation}\\label{eq:bce}\n\\mathcal{L} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{y}_i + (1-y_i)\\log(1-\\hat{y}_i)\\right],\\quad w_i = \\begin{cases} r & y_i=1 \\\\ 1 & y_i=0 \\end{cases}\n\\end{equation}\nFor the IBM benchmark $r\\approx 5.2$, upweighting minority-class contributions. Parameters are updated with Adam \\citep{kingma_adam} ($\\eta=5\\times 10^{-3}$, $L_2$ decay $\\lambda=10^{-3}$), full-batch for up to 600 epochs with early stopping on a stratified 20\\% internal validation split (patience 50 epochs, minimum improvement $10^{-4}$ AUC).\n\n\\subsubsection{Seed Bagging (KAN-Bag)}\n\nA single KAN-Net exhibited nontrivial initialization-dependent variance. KAN-Bag averages probabilities from $S=3$ KAN-Net instances trained with distinct seeds $s\\in\\{42,202,777\\}$:\n\\begin{equation}\\label{eq:kanbag}\n\\hat{p}_{\\text{KAN-Bag}}(\\mathbf{x}) = \\frac{1}{S}\\sum_{s=1}^{S} \\hat{y}_s(\\mathbf{x}).\n\\end{equation}\nBy the bias--variance decomposition, if $S$ models have equal bias and pairwise error correlation $\\rho$, bagged variance is $\\sigma^2/S\\cdot[1+(S-1)\\rho]$, decreasing approximately as $1/S$ for small $\\rho$. In the component ablation (Table~\\ref{tab:ablation_components}), seed bagging raised AUC from $0.8227$ to $0.8391$---a contribution comparable to feature engineering---demonstrating that initialization variance is a primary challenge for small-dataset KAN training.\n\n\\subsection{KASTLE-X: KAN-Augmented Stacking Ensemble}\n\n\\subsubsection{Base-Learner Pool}\n\nKASTLE-X maintains a pool $\\mathcal{P}$ of $K=8$ base learners: $\\mathcal{P} = \\{\\text{LightGBM}^\\star, \\text{XGBoost}^\\star, \\text{CatBoost}, \\text{HistGB}, \\text{RF}, \\text{ExtraTrees}, \\text{LR}, \\text{KAN-Bag}\\}$, where $\\star$ denotes per-fold Bayesian optimization. This spans histogram-based gradient boosting \\citep{ke_lightgbm, chen_xgboost}, ordered boosting \\citep{prokhorenkova_catboost}, variance-reduction ensembles, a linear boundary model, and the proposed KAN architecture, maximizing conditional independence of base-learner errors. An architecture diagram of the complete KASTLE-X pipeline---from raw data through feature engineering, base learners, OOF meta-features, and meta-learner---is shown in Figure~\\ref{fig:pipeline}.\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{f4992235-9dd8-4ac0-8094-9c3d78ca4a1e.png}\n\\end{center}\n\\caption{KASTLE-X architecture diagram. Raw features are combined with 12 leakage-free engineered features to form a 63-feature design matrix. In each outer fold, base learners generate out-of-fold (OOF) meta-features on the training partition; the logistic meta-learner is trained on these OOF features. At inference time all base learners are refit on the full training partition and the meta-learner combines their predictions. The KAN-Bag component is highlighted to distinguish it from the conventional learners.}\\label{fig:pipeline}\n\\end{figure}\n\n\\subsubsection{Leakage-Free Out-of-Fold Meta-Features}\n\nLet $\\mathcal{D}=\\{(\\mathbf{x}_i,y_i)\\}_{i=1}^{N}$ be the training data for a given outer fold. Partition $\\mathcal{D}$ into $K_{\\text{in}}=5$ inner folds. For each inner fold $t$ with training set $\\mathcal{D}_t^{\\text{tr}}$ and validation set $\\mathcal{D}_t^{\\text{va}}$, train each base learner $b_k$ on $\\mathcal{D}_t^{\\text{tr}}$ and predict on $\\mathcal{D}_t^{\\text{va}}$. Each training example receives a prediction from a model never fit on it, yielding the leakage-free meta-feature matrix $\\mathbf{Z}\\in\\mathbb{R}^{N\\times K}$:\n\\begin{equation}\\label{eq:oof}\nZ_{i,k} = b_k^{\\,\\backslash t(i)}(\\mathbf{x}_i), \\quad i=1,\\ldots,N,\\ k=1,\\ldots,K.\n\\end{equation}\n\n\\subsubsection{Class-Weighted Logistic Meta-Learner}\n\nThe meta-learner is a class-balanced logistic regression with $L_2$ regularization:\n\\begin{equation}\\label{eq:meta_lr}\n\\hat{p}_{\\text{meta}}(\\mathbf{z}) = \\sigma(\\mathbf{w}^\\top\\mathbf{z} + b), \\quad \\mathbf{w}\\in\\mathbb{R}^K,\\ b\\in\\mathbb{R},\n\\end{equation}\n\\begin{equation}\\label{eq:meta_loss}\n\\mathcal{L}_{\\text{meta}} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{p}_{\\text{meta}}(\\mathbf{z}_i) + (1-y_i)\\log(1-\\hat{p}_{\\text{meta}}(\\mathbf{z}_i))\\right] + \\lambda\\lVert\\mathbf{w}\\rVert_2^2.\n\\end{equation}\nLogistic regression is chosen as the meta-learner for four reasons: (i) convexity guarantees convergence; (ii) the weight vector $\\mathbf{w}$ provides directly interpretable attribution of each base learner's marginal contribution; (iii) under super-learner theory \\citep{vanderlaan_superlearner}, a logistic meta-learner is asymptotically optimal among convex combinations for log-loss risk; and (iv) empirically, on this dataset size ($N\\approx 1{,}176$ training samples per outer fold), logistic meta-learners outperformed MLP and KAN-residual meta-learners. Note that the logistic meta-learner operates on the base learners' predicted \\emph{probabilities} rather than on original features; as such, its weight vector explains the ensemble-level combination, not feature-level influence, which is the role of the TreeSHAP analysis in Section~\\ref{sec:shap}.\n\n\\subsubsection{F1-Optimal Threshold Selection}\n\nThe default threshold $\\tau=0.5$ is inappropriate at 16\\% prevalence. For each outer fold, the threshold is selected on inner-OOF meta-predictions:\n\\begin{equation}\\label{eq:thresh}\n\\tau^* = \\argmax_{\\tau\\in(0,1)}\\ \\text{F1}\\!\\left(\\mathbf{y},\\mathbb{1}\\{\\hat{p}_{\\text{meta}}(\\mathbf{z})\\geq\\tau\\}\\right).\n\\end{equation}\nBecause $\\tau^*$ is computed entirely within the training partition, it introduces no optimistic bias.\n\n\\subsection{Hyperparameter Optimization}\n\nLightGBM and XGBoost are optimized per outer fold using Optuna's Tree-structured Parzen Estimator (TPE) \\citep{akiba_optuna}. The complete hyperparameter search spaces and final selected values are provided in Table~\\ref{tab:hyperparams}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Hyperparameter search spaces and representative final selected values for LightGBM and XGBoost (per outer fold via Optuna TPE, 25 trials, 3-fold inner CV AUC objective). All other pool members use fixed configurations listed in the Supplementary Material.}\\label{tab:hyperparams}\n\\footnotesize\n\\begin{tabular}{lllr}\n\\toprule\n\\textbf{Model} & \\textbf{Hyperparameter} & \\textbf{Search Range} & \\textbf{Typical Selected} \\\\\n\\midrule\nLightGBM & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 390 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.063 \\\\\n & \\texttt{num\\_leaves} & $[15, 63]$ (int) & 31 \\\\\n & \\texttt{min\\_child\\_samples} & $[10, 60]$ (int) & 24 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.82 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.75 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 0.48 \\\\\n\\midrule\nXGBoost & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 420 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.055 \\\\\n & \\texttt{max\\_depth} & $[3, 8]$ (int) & 5 \\\\\n & \\texttt{min\\_child\\_weight} & $[1, 10]$ (int) & 3 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.79 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.71 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 1.24 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nRegarding imbalance handling: boosting models (LightGBM, XGBoost, CatBoost, HistGB) incorporate class-imbalance handling natively via their split-gain criteria (through \\texttt{scale\\_pos\\_weight} or \\texttt{class\\_weight}), and no additional resampling is applied because our ablation (Table~\\ref{tab:imbalance}) confirmed that SMOTE/ADASYN degraded AUC for GBDT learners on this dataset. For tree ensembles (RF, ExtraTrees) and logistic regression, explicit \\texttt{class\\_weight=\"balanced\"} is used. We note that no multiple-comparison correction is applied to the statistical tests in Table~\\ref{tab:stats}, as each comparison is a pre-specified pairwise test of a distinct ensemble configuration against KASTLE-X; we report raw $p$-values and encourage readers to interpret them conservatively.\n\n\\subsection{Evaluation Protocol}\n\nThe protocol is fully nested to eliminate all known leakage pathways. The outer loop uses 5-fold stratified CV (seed 42); the inner loop uses 5-fold stratified CV within each outer training partition. Within a single outer fold: (i) outer split; (ii) inner-OOF generation of $\\mathbf{Z}$; (iii) Optuna tuning on the training partition; (iv) meta-learner training on $(\\mathbf{Z},\\mathbf{y}^{\\text{tr}})$; (v) isotonic calibration on OOF predictions (calibrated variant only); (vi) $\\tau^*$ selection via~\\eqref{eq:thresh}; (vii) refit of all base learners on the full training partition; (viii) test inference; (ix) metric computation. Steps (ii)--(vi) are strictly confined to $\\mathcal{D}^{\\text{tr}}$; only step (ix) accesses $\\mathcal{D}^{\\text{te}}$.\n\nReported metrics: ROC-AUC, PR-AUC, F1, balanced accuracy, MCC, and Brier score as mean $\\pm$ std across five outer folds. Fold-wise AUC differences are assessed with the paired $t$-test and Wilcoxon signed-rank test ($n=5$; the attainable Wilcoxon minimum is $p=0.0625$).\n\n\n%===================================================================\n\\section{Results}\\label{sec:results}\n%===================================================================\n\n\\subsection{Exploratory Analysis}\n\nThe class distribution is markedly imbalanced (Figure~\\ref{fig:class}). Kernel-density comparisons show leavers concentrated at younger ages, lower incomes, and shorter tenures (Figure~\\ref{fig:kde}). Categorical breakdowns show elevated attrition among overtime workers, frequent travelers, single employees, and sales roles; ordinal engagement variables show monotone gradients where attrition declines as satisfaction and involvement increase (Figures~\\ref{fig:cat} and~\\ref{fig:ordinal}). Risk is front-loaded in the first one to three years (Figure~\\ref{fig:tenure}). Mutual-information analysis confirms that six of the twelve engineered features appear in the top-20 ranking, with \\textsc{OverTimeStress} ($f_{10}$) the second most informative feature overall (Figures~\\ref{fig:mi} and~\\ref{fig:mieng}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.5\\linewidth]{Screenshot_77.png}\n\\end{center}\n\\caption{Class distribution of the attrition label (prevalence $= 0.161$, $n=1{,}470$).}\\label{fig:class}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_78.png}\n\\end{center}\n\\caption{Kernel-density comparisons of key numeric features by attrition status.}\\label{fig:kde}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_76.png}\n\\end{center}\n\\caption{Attrition rates across categorical features.}\\label{fig:cat}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_79.png}\n\\end{center}\n\\caption{Attrition rate across ordinal engagement variables.}\\label{fig:ordinal}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_75.png}\n\\end{center}\n\\caption{Attrition rate by tenure bins.}\\label{fig:tenure}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_73.png}\n\\end{center}\n\\caption{Top-20 features by mutual information, including engineered features.}\\label{fig:mi}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_74.png}\n\\end{center}\n\\caption{Mutual-information ranking restricted to the twelve engineered features.}\\label{fig:mieng}\n\\end{figure}\n\n\\subsection{Imbalance-Handling Ablation}\n\nA preliminary ablation evaluated four strategies on a fixed LightGBM learner under 5-fold stratified CV (Table~\\ref{tab:imbalance}). No resampling achieved the highest AUC ($0.8125$), consistent with prior findings that SMOTE distorts GBDT decision boundaries. Main experiments therefore use no resampling for boosting models and balanced class weights for tree ensembles and logistic regression.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Imbalance-handling ablation on a fixed LightGBM learner ($5$-fold, mean $\\pm$ std). All resampling is applied strictly within training folds.}\\label{tab:imbalance}\n\\begin{tabular}{lccc}\n\\toprule\n\\textbf{Strategy} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} \\\\\n\\midrule\nNone (raw) & $0.8125 \\pm 0.023$ & $0.5639 \\pm 0.047$ & $0.4358 \\pm 0.050$ \\\\\nClass weighting (balanced) & $0.8109 \\pm 0.029$ & $0.5612 \\pm 0.055$ & $0.4547 \\pm 0.044$ \\\\\nSMOTE (within-fold) & $0.8014 \\pm 0.019$ & $0.5490 \\pm 0.052$ & $0.4350 \\pm 0.047$ \\\\\nADASYN (within-fold) & $0.8035 \\pm 0.019$ & $0.5547 \\pm 0.047$ & $0.4376 \\pm 0.033$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Individual Model Benchmark}\n\nTwenty classifiers were evaluated on the 63-feature design matrix under 5-fold stratified CV (Table~\\ref{tab:zoo}, Figure~\\ref{fig:zoo}). \\textbf{KAN-Bag achieves the highest AUC ($0.8485$), PR-AUC ($0.6354$), F1 ($0.5945$), balanced accuracy ($0.7780$), and MCC ($0.5131$) among all 20 individual classifiers.} Minority-class precision is 0.630 and minority-class recall is 0.562. The second-best on AUC is LDA ($0.8267$). All four GBDT variants are outperformed by KAN-Bag at the zoo-evaluation stage; they perform substantially better as pool members after per-fold Bayesian tuning.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Individual model benchmark on engineered features ($5$-fold, mean $\\pm$ std). Best value per metric in bold. Minority-class (attrition=Yes) Prec./Rec.\\ are for information at the F1-optimal threshold.}\\label{tab:zoo}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Model} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Min.Prec} & \\textbf{Min.Rec} \\\\\n\\midrule\n\\textbf{KAN-Bag (proposed)} & $\\mathbf{0.8485 \\pm 0.027}$ & $\\mathbf{0.6354 \\pm 0.057}$ & $\\mathbf{0.5945 \\pm 0.044}$ & $\\mathbf{0.7780 \\pm 0.020}$ & $\\mathbf{0.5131 \\pm 0.053}$ & $\\mathbf{0.630}$ & $0.562$ \\\\\nLDA & $0.8267 \\pm 0.026$ & $0.6300 \\pm 0.059$ & $0.5548 \\pm 0.076$ & $0.7126 \\pm 0.042$ & $0.5032 \\pm 0.081$ & $0.544$ & $0.566$ \\\\\nLogistic Regression & $0.8247 \\pm 0.024$ & $0.5952 \\pm 0.044$ & $0.4857 \\pm 0.015$ & $0.7400 \\pm 0.017$ & $0.3801 \\pm 0.024$ & $0.471$ & $0.501$ \\\\\nLinear SVM & $0.8235 \\pm 0.026$ & $0.6015 \\pm 0.049$ & $0.3703 \\pm 0.068$ & $0.6153 \\pm 0.027$ & $0.4007 \\pm 0.064$ & $0.641$ & $0.262$ \\\\\nRandom Forest & $0.8227 \\pm 0.041$ & $0.5775 \\pm 0.068$ & $0.4471 \\pm 0.044$ & $0.6522 \\pm 0.020$ & $0.4115 \\pm 0.063$ & $0.468$ & $0.428$ \\\\\nKAN-Net (single) & $0.8227 \\pm 0.016$ & $0.5790 \\pm 0.059$ & $0.5426 \\pm 0.061$ & $0.7508 \\pm 0.043$ & $0.4483 \\pm 0.076$ & $0.547$ & $0.539$ \\\\\nSVM (RBF) & $0.8200 \\pm 0.026$ & $0.5799 \\pm 0.039$ & $0.4797 \\pm 0.025$ & $0.6664 \\pm 0.014$ & $0.4540 \\pm 0.024$ & $0.502$ & $0.458$ \\\\\nAdaBoost & $0.8198 \\pm 0.029$ & $0.5965 \\pm 0.056$ & $0.4895 \\pm 0.057$ & $0.6733 \\pm 0.026$ & $0.4494 \\pm 0.073$ & $0.491$ & $0.489$ \\\\\nExtra Trees & $0.8146 \\pm 0.025$ & $0.5729 \\pm 0.066$ & $0.5063 \\pm 0.051$ & $0.6903 \\pm 0.021$ & $0.4366 \\pm 0.074$ & $0.508$ & $0.504$ \\\\\nCatBoost & $0.8115 \\pm 0.026$ & $0.5934 \\pm 0.037$ & $0.4262 \\pm 0.051$ & $0.6409 \\pm 0.024$ & $0.4160 \\pm 0.041$ & $0.434$ & $0.419$ \\\\\nBagging (DT) & $0.8039 \\pm 0.031$ & $0.5431 \\pm 0.034$ & $0.4362 \\pm 0.051$ & $0.6470 \\pm 0.023$ & $0.3990 \\pm 0.071$ & $0.440$ & $0.433$ \\\\\nHistGB & $0.8035 \\pm 0.025$ & $0.5507 \\pm 0.048$ & $0.4286 \\pm 0.047$ & $0.6435 \\pm 0.024$ & $0.4013 \\pm 0.035$ & $0.435$ & $0.423$ \\\\\nGradient Boosting & $0.8029 \\pm 0.016$ & $0.5528 \\pm 0.015$ & $0.4372 \\pm 0.060$ & $0.6509 \\pm 0.031$ & $0.3918 \\pm 0.045$ & $0.439$ & $0.435$ \\\\\nLightGBM & $0.8022 \\pm 0.036$ & $0.5521 \\pm 0.048$ & $0.4227 \\pm 0.064$ & $0.6414 \\pm 0.030$ & $0.3980 \\pm 0.050$ & $0.425$ & $0.420$ \\\\\nXGBoost & $0.7999 \\pm 0.026$ & $0.5570 \\pm 0.042$ & $0.4211 \\pm 0.039$ & $0.6390 \\pm 0.016$ & $0.3962 \\pm 0.062$ & $0.423$ & $0.419$ \\\\\nGaussian NB & $0.7841 \\pm 0.041$ & $0.4775 \\pm 0.037$ & $0.4562 \\pm 0.024$ & $0.7226 \\pm 0.022$ & $0.3431 \\pm 0.035$ & $0.349$ & $0.659$ \\\\\nMLP & $0.7833 \\pm 0.042$ & $0.5438 \\pm 0.057$ & $0.4591 \\pm 0.053$ & $0.6695 \\pm 0.028$ & $0.3717 \\pm 0.062$ & $0.460$ & $0.459$ \\\\\nKNN & $0.7775 \\pm 0.044$ & $0.4681 \\pm 0.060$ & $0.1874 \\pm 0.048$ & $0.5515 \\pm 0.014$ & $0.2768 \\pm 0.037$ & $0.387$ & $0.120$ \\\\\nQDA & $0.7516 \\pm 0.035$ & $0.4326 \\pm 0.056$ & $0.4524 \\pm 0.019$ & $0.6923 \\pm 0.016$ & $0.3320 \\pm 0.025$ & $0.345$ & $0.662$ \\\\\nDecision Tree & $0.6666 \\pm 0.038$ & $0.3498 \\pm 0.020$ & $0.4154 \\pm 0.033$ & $0.6697 \\pm 0.027$ & $0.2825 \\pm 0.045$ & $0.409$ & $0.422$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_72.png}\n\\end{center}\n\\caption{Individual model benchmark ($5$-fold stratified CV). KAN-Bag attains the highest AUC among all twenty individual classifiers.}\\label{fig:zoo}\n\\end{figure}\n\n\\subsection{Ensemble Comparison}\n\nNested-CV results for six ensemble variants are presented in Table~\\ref{tab:ensembles}. KASTLE-X achieves AUC $0.8449\\pm0.020$, PR-AUC $0.6570\\pm0.051$, and F1 $0.5831\\pm0.035$. Minority-class recall is 59.5\\% and minority-class precision is 62.4\\%.\n\n\\textbf{Reframing KASTLE-X's contribution (per Reviewer 2).} KAN-Bag is the strongest individual classifier, and KASTLE-X does not surpass KAN-Bag on AUC ($0.8449$ vs.\\ $0.8485$). The contribution of KASTLE-X lies elsewhere: the ensemble improves over the non-KAN stacking baseline (Stacking-LR no KAN, $0.8335$ AUC) by $+0.0114$ AUC and $+0.0698$ F1, and it achieves this consistently on all five outer folds. KASTLE-X should therefore be understood not as a universally superior predictor, but as evidence that \\emph{KAN augmentation within stacking provides incremental value beyond a conventional pool of seven learners}. Whether a practitioner prefers KAN-Bag (simpler, slightly higher AUC) or KASTLE-X (higher F1, better PR-AUC) depends on the operational cost structure.\n\n\\begin{table}[h!]\n\\centering\n\\caption{KASTLE-X ensemble comparison, nested $5$-fold CV (mean $\\pm$ std). Model complexity is shown as approximate total parameter count / training time relative to Stacking-LR (no KAN).}\\label{tab:ensembles}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Method} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Brier} & \\textbf{Rel.\\,Time} \\\\\n\\midrule\n\\textbf{KASTLE-X (proposed)} & $\\mathbf{0.8449 \\pm 0.020}$ & $\\mathbf{0.6570 \\pm 0.051}$ & $\\mathbf{0.5831 \\pm 0.035}$ & $0.7574 \\pm 0.030$ & $\\mathbf{0.5054 \\pm 0.036}$ & $0.1424 \\pm 0.021$ & $1.0\\times$ \\\\\nKASTLE-X + isotonic & $0.8410 \\pm 0.021$ & $0.6276 \\pm 0.056$ & $0.5831 \\pm 0.035$ & $0.7574 \\pm 0.030$ & $0.5054 \\pm 0.036$ & $\\mathbf{0.0918 \\pm 0.010}$ & $1.0\\times$ \\\\\nKASTLE-X KANres meta & $0.8422 \\pm 0.026$ & $0.6543 \\pm 0.049$ & $0.5665 \\pm 0.058$ & $0.7483 \\pm 0.041$ & $0.4865 \\pm 0.063$ & $0.1414 \\pm 0.029$ & $1.1\\times$ \\\\\nRank-average voting & $0.8388 \\pm 0.025$ & $0.6382 \\pm 0.061$ & $0.5665 \\pm 0.043$ & $0.7452 \\pm 0.034$ & $0.4844 \\pm 0.049$ & $0.2344 \\pm 0.007$ & $0.9\\times$ \\\\\nSoft voting & $0.8404 \\pm 0.023$ & $0.6338 \\pm 0.058$ & $0.5215 \\pm 0.025$ & $0.6918 \\pm 0.012$ & $0.4764 \\pm 0.048$ & $0.0956 \\pm 0.008$ & $0.9\\times$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $0.8335 \\pm 0.021$ & $0.6382 \\pm 0.055$ & $0.5133 \\pm 0.032$ & $\\mathbf{0.7541 \\pm 0.026}$ & $0.4135 \\pm 0.044$ & $0.1550 \\pm 0.012$ & $0.7\\times$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_71.png}\n\\end{center}\n\\caption{ROC curves for KASTLE-X and comparison ensembles on pooled OOF predictions.}\\label{fig:roc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_70.png}\n\\end{center}\n\\caption{Precision--recall curves; dashed line marks the prevalence baseline (0.161).}\\label{fig:pr}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_69.png}\n\\end{center}\n\\caption{Fold-wise AUC across five outer folds. KASTLE-X exceeds Stacking-LR (no KAN) on every fold.}\\label{fig:foldauc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.65\\linewidth]{Screenshot_68.png}\n\\end{center}\n\\caption{Ensemble learning curve (diagnostic). Validation AUC continues to improve modestly with additional training examples, indicating performance is not saturated at $n=1{,}470$.}\\label{fig:learning}\n\\end{figure}\n\n\\subsection{Ablation and Statistical Tests}\n\n\\subsubsection{KAN Augmentation Ablation}\n\nKASTLE-X vs.\\ Stacking-LR (no KAN) on fold-wise AUC:\n\n\\begin{center}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Fold} & \\textbf{KASTLE-X} & \\textbf{Stacking-LR (no KAN)} \\\\\n\\midrule\n1 & 0.8327 & 0.8277 ($+0.0050$) \\\\\n2 & 0.8356 & 0.8209 ($+0.0147$) \\\\\n3 & 0.8746 & 0.8642 ($+0.0104$) \\\\\n4 & 0.8567 & 0.8451 ($+0.0116$) \\\\\n5 & 0.8251 & 0.8097 ($+0.0154$) \\\\\n\\midrule\nMean $\\pm$ SD & $0.8449\\pm0.020$ & $0.8335\\pm0.021$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\nThe AUC difference is positive on every fold; paired $t(4)=5.85$, $p=0.0036$ (95\\% CI for $\\Delta$AUC: $[0.0057,\\ 0.0172]$). The Wilcoxon signed-rank test yields $p=0.0625$ (minimum attainable with $n=5$ pairs). The discrepancy between the two tests is expected: with only five pairs, the paired $t$-test leverages the magnitude of differences whereas the Wilcoxon test uses only signs; both are consistent with a real but small effect, and inferential claims are explicitly qualified by $n=5$ in this paper.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Fold-wise statistical comparison ($n=5$ folds). Paired $t$-test and Wilcoxon signed-rank $p$-values on AUC. 95\\% confidence intervals for mean fold-wise $\\Delta$AUC are shown.}\\label{tab:stats}\n\\begin{tabular}{lcccc}\n\\toprule\n\\textbf{Comparison (KASTLE-X vs.)} & $\\boldsymbol{\\Delta}$\\textbf{AUC} & \\textbf{95\\% CI} & \\textbf{Paired $t$ $p$} & \\textbf{Wilcoxon $p$} \\\\\n\\midrule\nKASTLE-X + isotonic & $+0.0039$ & $[0.0028,\\ 0.0049]$ & $0.0001$ & $0.0625$ \\\\\nKASTLE-X KANres meta & $+0.0027$ & $[-0.0073,\\ 0.0127]$ & $0.5517$ & $1.0000$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $\\mathbf{+0.0114}$ & $\\mathbf{[0.0057,\\ 0.0172]}$ & $\\mathbf{0.0036}$ & $\\mathbf{0.0625}$ \\\\\nSoft voting & $+0.0045$ & $[0.0009,\\ 0.0082]$ & $0.0239$ & $0.0625$ \\\\\nRank-average voting & $+0.0061$ & $[-0.0035,\\ 0.0157]$ & $0.1619$ & $0.1875$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsubsection{Statistical Justification for the AUC Gain (Reviewer 3)}\n\nReviewer 3 raises the question of whether a $0.0114$ AUC gain is meaningful given only 237 positive observations. We address this at two levels. (1) \\emph{Statistical level}: the paired $t$-test detects a consistent within-fold improvement ($p=0.0036$) that is not attributable to sampling noise across folds; the 95\\% CI $[0.0057,\\ 0.0172]$ excludes zero. (2) \\emph{Practical level}: operationally, the F1 gain of $+0.0698$ translates directly to more correct attrition identifications per screening cycle. At the F1-optimal threshold, KASTLE-X correctly identifies 141 true positives compared with $\\approx 124$ for Stacking-LR (no KAN)---17 additional employees correctly flagged per full-workforce screening, reducing downstream replacement costs. We emphasize that these figures are illustrative for a synthetic benchmark and are not an organizational deployment study.\n\n\\subsection{Pooled Out-of-Fold Analysis}\n\nOn pooled OOF predictions (all 1{,}470 examples evaluated exactly once), KASTLE-X achieves AUC $=0.8404$, PR-AUC $=0.6432$, and at $\\tau^*=0.716$, F1 $=0.6091$. Confusion matrix: $[[1148,\\ 85],\\ [96,\\ 141]]$ (stayers/leavers predicted correctly on the diagonal). This yields sensitivity $=59.49\\%$, specificity $=93.11\\%$, precision $=62.39\\%$, false-positive rate $=6.89\\%$.\n\n\\textbf{Business translation (illustrative, synthetic benchmark).} A monthly screening of the full workforce would flag 226 employees (15.4\\%), of whom 141 are genuine attrition risks---a $3.7\\times$ enrichment over the 16.1\\% base attrition rate. At the F1-optimal threshold, the model would identify approximately 3 out of every 5 at-risk employees for proactive intervention. These figures are explicitly illustrative and should not be interpreted as deployment-ready estimates for any real organization, as the underlying dataset is synthetic.\n\n\\subsection{Meta-Learner Interpretability}\n\nThe logistic meta-learner coefficients trained on all 1{,}470 pooled OOF predictions provide a direct measure of each base learner's marginal contribution to the ensemble (Table~\\ref{tab:meta}). KAN-Bag receives the largest positive coefficient ($+2.5052$), followed by random forest ($+1.3778$) and logistic regression ($+1.1095$). The negative coefficients for LightGBM and HistGB reflect redundancy with other pool members, not individual harmfulness. The pool's prediction correlation matrix confirms KAN-Bag has the lowest average pairwise correlation with remaining pool members (Figure~\\ref{fig:pooldiv}), validating the architectural diversity argument.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Meta-learner coefficients from the logistic regression trained on all 1{,}470 pooled OOF predictions. A positive coefficient indicates a net positive marginal contribution; negative coefficients reflect redundancy with higher-weighted pool members.}\\label{tab:meta}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Base Learner} & \\textbf{Meta Coefficient} & \\textbf{Interpretation} \\\\\n\\midrule\nKAN-Bag & $+2.5052$ & Largest marginal contribution; architecturally distinct \\\\\nRandom Forest & $+1.3778$ & Strong independent variance reduction \\\\\nLogistic Regression & $+1.1095$ & Orthogonal linear signal \\\\\nCatBoost & $+0.7608$ & Distinct ordered-boosting signal \\\\\nXGBoost & $+0.5165$ & Moderate incremental value \\\\\nExtra Trees & $+0.2423$ & Small but positive incremental gain \\\\\nHistGB & $-0.1212$ & Redundant with LightGBM/XGBoost \\\\\nLightGBM & $-0.3363$ & Redundant with XGBoost/HistGB \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_67.png}\n\\end{center}\n\\caption{Pool prediction-correlation matrix. KAN-Bag has the lowest average pairwise correlation with remaining pool members, supporting the architectural diversity argument.}\\label{fig:pooldiv}\n\\end{figure}\n\n\\subsection{SHAP Interpretability}\\label{sec:shap}\n\nTreeSHAP was applied to the Optuna-tuned LightGBM learner (Figures~\\ref{fig:beeswarm} and~\\ref{fig:shapimp}). We note explicitly (per Reviewer 2) that this SHAP analysis explains the LightGBM \\emph{component} of KASTLE-X, not the full ensemble; it is positioned as component-level evidence for feature importance rather than ensemble-level attribution. The meta-learner coefficients (Table~\\ref{tab:meta}) and the prediction-diversity matrix (Figure~\\ref{fig:pooldiv}) provide the ensemble-level view.\n\nThe five most influential features are \\textsc{OverTime\\_Yes}, \\textsc{OverTimeStress} ($f_{10}$, engineered), \\textsc{MonthlyIncome}, \\textsc{IncomePerLevel} ($f_1$, engineered), and \\textsc{TotalWorkingYears}. Overtime exerts the largest single effect. The engineered $f_{10}$ provides complementary dose--response information beyond the binary indicator. Income features show a strong monotone negative relationship with attrition. These patterns are consistent across income, role, and tenure dimensions (Figures~\\ref{fig:dep_income}--\\ref{fig:dep_joblevel}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_66.png}\n\\end{center}\n\\caption{SHAP beeswarm summary for the tuned LightGBM component (not the full KASTLE-X ensemble). This analysis provides component-level feature attribution.}\\label{fig:beeswarm}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_65.png}\n\\end{center}\n\\caption{Mean absolute SHAP feature importance for the tuned LightGBM component.}\\label{fig:shapimp}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_61.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{MonthlyIncome}, coloured by overtime status.}\\label{fig:dep_income}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_63.png}\n\\end{center}\n\\caption{SHAP dependence plot for engineered \\textsc{IncomePerLevel} ($f_1$).}\\label{fig:dep_ipl}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_62.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{YearsAtCompany}, showing front-loaded early-tenure attrition risk.}\\label{fig:dep_years}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_64.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{JobLevel}, showing monotone decrease in attrition contribution with seniority.}\\label{fig:dep_joblevel}\n\\end{figure}\n\n\n%===================================================================\n\\section{Discussion}\\label{sec:discussion}\n%===================================================================\n\n\\subsection{Theoretical Significance}\n\nThis study contributes to two theoretical streams. First, it provides direct empirical evidence that KANs---whose learnable polynomial edge functions can represent monotone and non-monotone response curves flexibly---are architecturally distinctive from GBDTs on small-scale, noisy HR tabular data. Specifically, KAN-Bag achieves higher AUC than all four GBDT variants at the zoo benchmark stage, a result consistent with the hypothesis that the attitudinal Likert features in this dataset have response relationships better captured by polynomial bases than by axis-aligned splits. Second, the KAN-augmented stacking result confirms ensemble diversity theory \\citep{kuncheva_whitaker}: when a new learner's error correlations with an existing pool are lower than the pool's internal correlations, adding it improves the ensemble even when its standalone AUC is not highest, because the meta-learner can exploit its residual information.\n\n\\subsection{Empirical Contributions}\n\nThis study provides the most complete honest evaluation of the IBM HR attrition benchmark to date: 20 individual models, 6 ensemble variants, 7 performance metrics, formal statistical tests with confidence intervals, calibration analysis, and component ablation, all under a protocol that eliminates leakage. The comparison with published prior work on the same dataset, summarized in Table~\\ref{tab:prior}, illustrates the evaluation-protocol dependence of reported performance: studies using pre-split SMOTE report F1 values 25--50 percentage points above our honest estimates, confirming the data-leakage hypothesis of \\citet{rahman_review}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Comparison with published results on the IBM HR Analytics benchmark. Studies are ordered by reported AUC. All our results are from the current honest nested-CV evaluation. The protocol column flags the primary methodological concern.}\\label{tab:prior}\n\\footnotesize\n\\begin{tabular}{lcccp{4.2cm}}\n\\toprule\n\\textbf{Study} & \\textbf{Best Model} & \\textbf{Reported AUC} & \\textbf{Reported F1} & \\textbf{Evaluation Protocol} \\\\\n\\midrule\n\\citet{bibliometric_attrition_2025} & Ensemble & $\\sim$0.90 & $\\sim$0.88 & Pre-split SMOTE (leakage likely) \\\\\n\\citet{slr_attrition_2024} & XGBoost & $\\sim$0.87 & $\\sim$0.83 & Hold-out; pre-split oversampling \\\\\n\\citet{alqarni_power_bi_2025} & RF + BI & $\\sim$0.86 & $\\sim$0.81 & Single split; pre-split SMOTE \\\\\n\\textbf{This study} (KASTLE-X) & Stacking & $0.8449$ & $0.5831$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\textbf{This study} (KAN-Bag) & Individual & $0.8485$ & $0.5945$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Practical Implications}\n\nFor HR analytics practitioners, the results have several actionable implications. First, the $3.7\\times$ enrichment of the KASTLE-X screening list over the base attrition rate means that a limited number of HR interventions can be directed at the highest-risk employees, substantially improving the cost-effectiveness of retention programs. Second, the SHAP analysis identifies overtime load, income adequacy, and early tenure as the three primary attrition drivers in this benchmark; targeted interventions addressing these factors (flexible work arrangements, transparent compensation benchmarking, structured onboarding programs) may be more effective than generic engagement programs. Third, practitioners should select the decision threshold $\\tau^*$ based on the asymmetric costs of false positives (unnecessary retention spending) and false negatives (missed departures) in their organizational context, rather than using the default 0.5. Fourth, we emphasize that KASTLE-X is a predictive association model, not a causal intervention model: finding that overtime predicts attrition does not by itself prove that reducing overtime would reduce attrition, and causal claims require randomized field experiments.\n\n\\subsection{Research Limitations}\n\n\\textbf{Single-dataset scope.} The study uses one benchmark dataset representing one organization in a synthetic release. All performance figures are bounds on this specific benchmark; generalization to other organizational contexts, industries, or cultures requires external validation. In the absence of a second public HR attrition dataset with equivalent attributes, we clearly position this as a single-dataset limitation central to the conclusion.\n\n\\textbf{Statistical power.} Five outer folds limits the Wilcoxon test to its minimum $p=0.0625$. The paired $t$-test provides more power under the normality assumption but is sensitive to that assumption with $n=5$. Replication with ten-fold outer CV would provide more reliable inferences.\n\n\\textbf{Dataset size.} With 237 positive cases, the standard error on minority-class metrics is substantial. The component ablation results and fold-wise AUC differences are consistent but should be interpreted with this in mind.\n\n\\textbf{SHAP scope.} The SHAP analysis explains the LightGBM component, not the full ensemble. Full-ensemble attributions would require model-agnostic methods (e.g., LIME or Kernel SHAP) applied to the meta-learner output, which is a direction for future work.\n\n\\textbf{Causal interpretation.} Predictive associations identified by SHAP do not imply causal effects. The claim that overtime load predicts attrition is a predictive association, not evidence that reducing overtime would reduce attrition.\n\n\\subsection{Ethical Considerations and Responsible Deployment}\n\nAutomated attrition prediction tools carry several ethical risks that practitioners must address before deployment. First, even a well-calibrated model will produce false positives---employees flagged as at-risk who are not. If such flags influence managerial behavior (differential treatment, reduced promotion consideration), they may create self-fulfilling prophecies or constitute indirect discrimination. Second, the SHAP analysis shows that age and income are among the top predictors; if these are correlated with protected characteristics in a particular organization, the model may produce disparate-impact screening. Third, employees should be informed that such tools are in use and should have recourse to challenge model-generated assessments.\n\nSHAP-based explainability, as demonstrated in this paper, is a necessary but not sufficient mitigation: it enables identification of which features drive predictions, but does not verify that the model is fair across demographic subgroups, and does not substitute for organizational governance. We recommend that any deployment of systems like KASTLE-X include: (a) a fairness audit across age, gender, and ethnicity subgroups; (b) transparency with affected employees; (c) human oversight for any consequential decisions; and (d) regular re-evaluation as workforce composition and organizational context change.\n\n\\subsection{Future Research Directions}\n\n\\textbf{External validation.} The most important next step is evaluating KASTLE-X on additional organizational attrition datasets. We are not aware of a second public dataset with equivalent attribute richness for direct comparison; constructing or obtaining such a dataset is a valuable research contribution in itself.\n\n\\textbf{Full-ensemble interpretability.} Developing model-agnostic ensemble SHAP attributions that reflect the combined meta-learner output would align interpretability with the model actually deployed.\n\n\\textbf{Larger KAN pools.} As KAN research matures and computational costs decrease, adding multiple KAN variants (wavelet KAN, B-spline KAN) to the stacking pool may further increase diversity.\n\n\\textbf{Longitudinal validation.} A prospective validation study in which model-flagged employees are tracked over time would allow calibration of confidence intervals on the business-impact figures and provide causal evidence if combined with randomized retention interventions.\n\n\\textbf{Fairness-aware variants.} Adapting KASTLE-X with fairness constraints \\citep{lundberg_shap} on demographic parity or equalized odds would extend its applicability to contexts with stringent anti-discrimination requirements.\n\n\n%===================================================================\n\\section{Conclusion}\\label{sec:conclusion}\n%===================================================================\n\nThis paper presented KASTLE-X, a KAN-augmented stacking ensemble for employee attrition prediction. The primary contribution is a rigorous test of the hypothesis that an architecturally distinct KAN component---specifically KAN-Bag, a seed-bagged Chebyshev-polynomial KAN---provides incremental value within a heterogeneous stacking ensemble. The answer, clearly bounded to this single synthetic benchmark, is yes: KASTLE-X outperforms the identically structured non-KAN stacking ensemble on all five outer folds ($p=0.0036$; $\\Delta$AUC $=+0.0114$, 95\\% CI $[0.0057,\\ 0.0172]$; $\\Delta$F1 $=+0.0698$). The logistic meta-learner assigns KAN-Bag the largest coefficient ($2.51$), and the prediction-diversity analysis confirms that KAN-Bag's error correlations with the GBDT cluster are substantially lower than intra-GBDT correlations.\n\nThe narrower claim---that KAN augmentation within stacking \\emph{may} benefit tabular ensembles under class imbalance---is better grounded and more scientifically defensible than any claim of universal superiority. KAN-Bag is also the strongest of 20 individually benchmarked classifiers (AUC $0.8485$), outperforming CatBoost, XGBoost, LDA, and all other individual models. Twelve leakage-free engineered features confirmed by mutual-information analysis and SHAP interpretability (at the component level) add measurable informativeness. A component ablation isolates the contributions of feature engineering ($+0.030$ AUC), seed bagging ($+0.016$), and Bayesian optimization ($+0.009$).\n\nThe broader methodological contribution is the most complete honest evaluation of the IBM HR attrition benchmark to date, covering 20 models, 6 ensemble variants, 7 metrics, component ablation, calibration, statistical tests with confidence intervals, and SHAP interpretability under a strictly leakage-free nested protocol. These results advance both the practical toolkit for HR analytics and the nascent empirical literature on KAN applications to business tabular data.\n\n\n%===================================================================\n\\section*{Conflict of Interest Statement}\n%===================================================================\nThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n\\section*{Author Contributions}\nFA conceived the study, designed the KASTLE-X framework and KAN-Bag classifier, implemented the experimental pipeline, and drafted the manuscript. SA contributed to feature engineering design, statistical analysis, and manuscript revision. TA supervised the study, contributed to interpretation and SHAP analysis, and revised the manuscript. All authors read and approved the final manuscript.\n\n\\section*{Funding}\nThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\n\n\\section*{Acknowledgments}\nThe authors thank the maintainers of the open-source scientific Python ecosystem (scikit-learn, LightGBM, XGBoost, CatBoost, PyTorch, Optuna) and the three anonymous reviewers whose detailed critiques substantially improved the manuscript.\n\n\\section*{Supplemental Data}\n\\href{http://home.frontiersin.org/about/author-guidelines#SupplementaryMaterial}{Supplementary Material} accompanying this article contains: (S1) complete Python implementation of the KASTLE-X pipeline; (S2) per-fold hyperparameter selections for LightGBM and XGBoost; (S3) fixed hyperparameter configurations for all other pool members; (S4) additional interpretability figures; (S5) full numerical results for all 20 individual classifiers and 6 ensemble variants.\n\n\\section*{Data Availability Statement}\nThe IBM HR Analytics Employee Attrition \\& Performance dataset is publicly available at \\url{https://www.kaggle.com/datasets/pavansubhasht/ibm-hr-analytics-attrition-dataset}. All code required to reproduce the reported results is provided as supplementary material.\n\n\\bibliographystyle{Frontiers-Harvard}\n\\bibliography{test_revised}\n\n\\end{document}",
      "tex_filename": "frontiers.tex",
      "bib_content": "@article{Paul2026,\n  title={KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction},\n  author={Nirodh Paul and Md. Mahedi Hassan and Sumnoon Ferdous and Md. Masuqul Haque and Mir Mohammad Azad},\n  journal={Frontiers in Artificial Intelligence},\n  doi={10.3389/frai.2026.3861612},\n  year={2026}\n}\n",
      "source_dir": "/journals/artificial-intelligence/articles/10.3389/frai.2026.3861612/source",
      "tex_file": "/journals/artificial-intelligence/articles/10.3389/frai.2026.3861612/source/article.tex",
      "bib_file": "/journals/artificial-intelligence/articles/10.3389/frai.2026.3861612/source/references.bib",
      "id": "art_3861612",
      "updated_at": "2026-11-07T11:08:28Z",
      "created_at": "2026-11-07T11:08:28Z"
    },
    {
      "title": "KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction",
      "authors": [
        {
          "name": "Nirodh Paul",
          "affiliations": [
            "1"
          ],
          "is_corresponding": false,
          "affil_str": "1",
          "initials": "NP"
        },
        {
          "name": "Md. Mahedi Hassan",
          "affiliations": [
            "2"
          ],
          "is_corresponding": false,
          "affil_str": "2",
          "initials": "MH"
        },
        {
          "name": "Sumnoon Ferdous",
          "affiliations": [
            "3"
          ],
          "is_corresponding": false,
          "affil_str": "3",
          "initials": "SF"
        },
        {
          "name": "Md. Masuqul Haque",
          "affiliations": [
            "4"
          ],
          "is_corresponding": false,
          "affil_str": "4",
          "initials": "MH"
        },
        {
          "name": "Mir Mohammad Azad",
          "affiliations": [
            "5"
          ],
          "is_corresponding": false,
          "affil_str": "5",
          "initials": "MA"
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh"
        },
        {
          "index": "2",
          "text": "Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh"
        },
        {
          "index": "3",
          "text": "Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh"
        },
        {
          "index": "4",
          "text": "Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh"
        },
        {
          "index": "5",
          "text": "Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh"
        }
      ],
      "corr_author": "",
      "corr_email": "kotpiuznd141@hotmail.com",
      "abstract": "Employee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov\u2013Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds incremental value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12% positive prevalence) under a nested 5{\u00d7}5-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC (0.8485 \u00b1 0.0266) and F1 (0.5945). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by +0.0114 (p = 0.0036, paired t-test; Wilcoxon minimum p = 0.0625, n=5 folds), PR-AUC by +0.0188, and F1 by +0.0698 on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the 0.0114 AUC gain\u2014achieved with only 237 positive cases\u2014against its practical screening benefit (3.7\u00d7 enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov\u2013Arnold networks provide distinct diversity that may benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.",
      "keywords": "employee attrition; Kolmogorov\u2013Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning",
      "doi": "10.3389/fmed.2026.19868346",
      "article_url_path": "/journals/medicine/articles/10.3389/fmed.2026.1986834/abstract",
      "journal_slug": "medicine",
      "journal": "Frontiers in Medicine",
      "journal_abbrev": "Front. Med.",
      "section": "Sec. Precision Medicine",
      "banner": "/assets/images/journals/medicine-banner.png",
      "issn": "2296-858X",
      "impact_factor": "3.6",
      "citescore": "5.4",
      "received": "2026-10-20",
      "accepted": "2026-11-01",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
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      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Revised manuscript: KASTLE-X \u2014 Major Revision addressing Reviewers 1, 2, and 3\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%% Version 3.4 Generated 2022/06/14 %%%\n\\documentclass[utf8]{FrontiersinHarvard}\n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\\usepackage{amsmath,amssymb,booktabs,array,xcolor}\n\n\\linenumbers\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\\def\\firstAuthorLast{Author {et~al.}}\n\\def\\Authors{Nirodh Paul\\,$^{1}$, Md. Mahedi Hassan\\,$^{2}$, Sumnoon Ferdous\\,$^{3}$, Md. Masuqul Haque\\,$^{4}$ and Mir Mohammad Azad\\,$^{5}$}\n\\def\\Address{$^{1}$Department of Accounting and Information Systems, University of Barishal, Barishal, Bangladesh \\\\\n$^{2}$Department of Software Engineering, Daffodil International University, Dhaka, Bangladesh \\\\\n$^{3}$Department of Management Information Systems, Independent University Bangladesh, Dhaka, Bangladesh \\\\\n$^{4}$Department of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh \\\\\n$^{5}$Department of Computer Science and Engineering, Uttara University, Turag, Uttara, Dhaka-1230, Bangladesh}\n\n\\def\\corrAuthor{}\n\\def\\corrEmail{kotpiuznd141@hotmail.com}\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title[KASTLE-X for Employee Attrition Prediction]{KASTLE-X: Incremental Value of Kolmogorov--Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction}\n\n\\author[\\firstAuthorLast]{\\Authors}\n\\address{}\n\\correspondance{}\n\\extraAuth{}\n\n\\maketitle\n\n%-------------------------------------------------------------------\n\\begin{abstract}\n\\section{}\n\nEmployee attrition prediction from routine personnel records is a canonical imbalanced tabular classification problem. We propose KASTLE-X (Kolmogorov--Arnold Network-Augmented Stacked Learning Ensemble with leakage-free feature engineering) and investigate whether an architecturally novel KAN component adds \\emph{incremental} value to a conventional stacking ensemble of Bayesian-optimized tabular learners. The framework is evaluated on the IBM HR Analytics Employee Attrition benchmark (1{,}470 records, 16.12\\% positive prevalence) under a nested $5{\\times}5$-fold stratified cross-validation protocol in which all preprocessing, hyperparameter optimization, meta-feature generation, calibration, and threshold selection are confined strictly to training partitions. We first benchmark 20 individual classifiers spanning eight algorithmic families; KAN-Bag, a seed-bagged Chebyshev-polynomial KAN, achieves the highest individual AUC ($0.8485 \\pm 0.0266$) and F1 ($0.5945$). We then establish that adding KAN-Bag to a seven-learner conventional stacking pool improves ensemble AUC by $+0.0114$ ($p = 0.0036$, paired $t$-test; Wilcoxon minimum $p = 0.0625$, $n=5$ folds), PR-AUC by $+0.0188$, and F1 by $+0.0698$ on every outer fold. The logistic meta-learner assigns KAN-Bag the largest coefficient (2.51), confirming its contribution arises from architectural diversity rather than raw accuracy alone. We contextualize the $0.0114$ AUC gain---achieved with only 237 positive cases---against its practical screening benefit ($3.7\\times$ enrichment over base rate) and against the power limits of five-fold testing, and we clearly bound all claims to this single synthetic benchmark. These results support the narrower but well-grounded conclusion that Kolmogorov--Arnold networks provide distinct diversity that \\emph{may} benefit tabular stacking ensembles under class imbalance, with external validation on other organizational datasets as a necessary future step.\n\n\\tiny\n \\keyFont{ \\section{Keywords:} employee attrition; Kolmogorov--Arnold networks; stacked ensemble learning; feature engineering; class imbalance; nested cross-validation; explainable AI; Bayesian optimization; tabular deep learning}\n\\end{abstract}\n\n\n%===================================================================\n\\section{Introduction}\n%===================================================================\n\n\\subsection{Research Context and Practical Motivation}\n\nVoluntary employee turnover is among the costliest operational events an organization can experience. Replacement expenditures are estimated at 50\\%--200\\% of a departing employee's annual salary \\citep{shrm_replacement_cost}, encompassing direct recruitment and onboarding costs as well as indirect costs from lost institutional knowledge and disrupted team cohesion. In large organizations, aggregate replacement costs readily reach tens of millions of dollars annually. Predictive analytics applied to routine HR records therefore represents a high-value operational intervention: identifying employees with elevated attrition risk in advance enables targeted engagement programs, compensation adjustments, or career-development conversations at a fraction of the replacement cost.\n\n\\subsection{Technical Challenges}\n\nThe machine-learning framing of attrition prediction is a binary classification task on a small, heterogeneous, highly imbalanced tabular dataset. Three structural properties make it genuinely challenging. First, the positive class is scarce: in the widely used IBM HR Analytics benchmark, only 237 of 1{,}470 employees (16.12\\%) left \\citep{ibm_dataset}. Second, the feature space mixes ordinal Likert scales, categorical job descriptors, and continuous financial variables whose marginal predictive power is modest after accounting for correlations. Third, the label contains substantial irreducible noise from personal events invisible in HR records, setting a genuine Bayes error floor. These properties cap achievable F1 at values that may seem moderate in absolute terms but represent genuine predictive value relative to the no-skill baseline.\n\n\\subsection{Methodological Gap}\n\nThe literature on attrition prediction is characterized by two concurrent weaknesses. First, published evaluations frequently report inflated performance because synthetic minority oversampling \\citep{chawla_smote} is applied before the train--test split, allowing synthetic copies of minority test samples to appear in training data \\citep{rahman_review}. Second, no published study has systematically examined whether Kolmogorov--Arnold Networks (KANs) \\citep{liu_kan}---a recently proposed architecture with learnable polynomial edge functions---add useful architectural diversity to stacking ensembles of conventional tabular learners. Architectural diversity is the primary mechanism through which stacking exceeds its constituent base learners \\citep{kuncheva_whitaker}, and dominant gradient-boosted decision tree (GBDT) variants in current pools often have prediction correlations exceeding 0.9, leaving limited room for meta-learner exploitation.\n\n\\subsection{Research Objectives}\n\nThis study addresses four objectives:\n\\begin{enumerate}\n  \\item[\\textbf{O1}] Establish a leakage-free benchmark of 20 individual classifiers spanning all major tabular algorithmic families on the engineered IBM HR dataset.\n  \\item[\\textbf{O2}] Develop KAN-Bag, a seed-bagged Chebyshev-polynomial KAN classifier, and quantify the separate contributions of the KAN architecture, seed bagging, and feature engineering through ablation.\n  \\item[\\textbf{O3}] Evaluate whether KAN-Bag provides statistically meaningful incremental value when added to a heterogeneous stacking ensemble (KASTLE-X vs.\\ Stacking-LR without KAN).\n  \\item[\\textbf{O4}] Characterize the practical limitations of the findings, including the single-dataset scope, small sample size, and implications for responsible HR deployment.\n\\end{enumerate}\n\n\\subsection{Contributions}\n\nAgainst these objectives, the specific contributions are: (i) \\emph{KAN-Bag}: a seed-bagged Chebyshev-polynomial KAN tabular classifier that achieves the highest individual AUC among 20 compared classifiers; (ii) \\emph{KASTLE-X}: a KAN-augmented stacking ensemble with a class-weighted logistic meta-learner, demonstrated to improve over the non-KAN stacking baseline on all five outer folds ($p=0.0036$); (iii) twelve leakage-free, domain-motivated engineered features confirmed by mutual-information analysis; (iv) a component ablation isolating the contributions of KAN architecture, seed bagging, and feature engineering; and (v) the most comprehensive honest evaluation of the IBM HR attrition benchmark to date, covering 20 individual models, 6 ensemble variants, 7 performance metrics, calibration analysis, statistical tests with explicitly bounded claims, and SHAP interpretability.\n\nThe remainder of the paper is organized as follows. Section~\\ref{sec:related} reviews related work. Section~\\ref{sec:methods} presents the dataset, exploratory analysis, feature engineering, KAN architecture, KASTLE-X framework, hyperparameter optimization, and evaluation protocol. Section~\\ref{sec:results} presents experimental results. Section~\\ref{sec:discussion} discusses findings, limitations, ethical considerations, and future directions. Section~\\ref{sec:conclusion} concludes.\n\n%===================================================================\n\\section{Literature Review}\\label{sec:related}\n%===================================================================\n\n\\subsection{Employee Attrition Prediction}\n\nEarly computational approaches to employee turnover used logistic regression and survival analysis. The democratization of the IBM HR Analytics dataset catalyzed a shift toward ML experimentation, with subsequent studies applying support vector machines, decision trees, random forests, gradient-boosting machines, and neural networks. \\citet{rahman_review} found that gradient-boosted ensembles---particularly XGBoost \\citep{chen_xgboost} and LightGBM \\citep{ke_lightgbm}---consistently produced the highest cross-validated AUC values (typically 0.80--0.87) when evaluation protocols were correctly specified.\n\nA pervasive concern is data leakage through synthetic oversampling. When SMOTE \\citep{chawla_smote} is applied before the train--test split, synthetic copies of test-set minority instances appear in training data, producing optimistic estimates. Under honest within-fold resampling on the IBM benchmark, F1 values of 0.45--0.55 are typical; published values of 0.80--0.90 in studies using pre-split SMOTE are leakage artifacts. The present study applies no resampling and restricts all processing to training partitions.\n\nMore recent work has explored deep learning for tabular attrition prediction. TabNet \\citep{arik_tabnet} uses sequential attention to select relevant features at each step. However, benchmarks such as \\citet{grinsztajn_trees} consistently find that well-tuned GBDTs match or outperform neural tabular architectures on small-to-medium datasets, a finding attributable to the inductive biases of tree ensembles: robustness to irrelevant features, implicit feature selection, and resistance to overparameterization. Explainability has emerged as a central concern in HR analytics; SHAP \\citep{lundberg_shap} provides consistent, locally additive feature attributions with game-theoretic foundations.\n\nRecent literature has also begun examining the impact of class-imbalance strategies in HR classification. \\citet{alqarni_power_bi_2025} demonstrated that ML models with power BI dashboards for attrition can aid managerial decision-making, and \\citet{bibliometric_attrition_2025} provided a bibliometric synthesis of ML methods for employee attrition prediction, identifying gradient boosting and neural networks as the most frequently applied approaches. \\citet{slr_attrition_2024} conducted a systematic literature review of quantitative attrition models, confirming that ensemble methods dominate recent publications but that rigorous leakage-free protocols remain underrepresented.\n\n\\subsection{Ensemble Learning and Stacking}\n\nBagging reduces variance by averaging predictions over bootstrap subsamples; boosting reduces bias through additive residual fitting; stacking \\citep{wolpert_stacking} trains a meta-learner on out-of-fold predictions from heterogeneous base learners. The meta-learner learns the optimal combination rather than assuming a fixed rule.\n\nDiversity of base learners is central to stacking's benefit: if all base learners make correlated errors, the meta-learner has no information to correct them. \\citet{kuncheva_whitaker} formalized this diversity--accuracy trade-off, showing that ensembles benefit most when base-learner errors are conditionally independent. Practical stacking implementations achieve diversity by combining learners with different inductive biases---linear models, kernel machines, tree ensembles, and neural architectures. However, GBDT variants dominate current tabular stacking pools, and their prediction correlations often exceed 0.9. Super-learner theory \\citep{vanderlaan_superlearner} provides asymptotic justification: under regularity conditions, the cross-validated stacked ensemble converges to the oracle model minimizing expected loss among all convex combinations of base learners.\n\n\\subsection{Kolmogorov--Arnold Networks and Tabular Deep Learning}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957, arnold_1963} establishes that any continuous $f:[0,1]^n\\to\\mathbb{R}$ can be written as a finite composition of continuous univariate functions and additions. \\citet{liu_kan} proposed KANs as a neural architecture inspired by this theorem, replacing fixed activations on nodes with learnable univariate functions on edges parameterized by B-splines. Subsequent work has explored alternative bases: \\citet{bozorgasl_wavkan} used wavelets; Chebyshev polynomial bases offer computational advantages through a stable three-term recurrence.\n\nThe current empirical state of KAN research for tabular classification reveals a nuanced picture. Early evidence from \\citet{liu_kan} demonstrated that KANs can match or exceed MLPs on scientific and regression tasks with fewer parameters. However, the broader tabular deep-learning literature---as surveyed in \\citet{grinsztajn_trees} and synthesized in \\citet{arik_tabnet}---consistently finds that GBDTs retain an advantage on small-to-medium tabular datasets due to their ability to handle irregular feature distributions, categorical variables, and uninformative features without specialized architectural inductive biases. KANs, like MLPs, lack these inductive biases, making their advantage domain-dependent. On small, imbalanced HR datasets---the focus of this paper---their behavior as standalone predictors and as ensemble components has received little systematic attention. This study contributes such an assessment.\n\n\n%===================================================================\n\\section{Materials and Methods}\\label{sec:methods}\n%===================================================================\n\n\\noindent\\textbf{Glossary.}\n\\begin{center}\n\\begin{tabular}{lp{0.72\\linewidth}}\n\\toprule\n\\textbf{Term} & \\textbf{Definition} \\\\\n\\midrule\nLeakage-free feature engineering & Features constructed as row-wise transformations that depend only on the individual observation and universal constants, with no reference to other rows, group statistics, or the target variable. \\\\\nNested cross-validation & A two-level CV protocol in which the outer loop evaluates model performance and the inner loop handles all model selection and tuning, ensuring outer test folds are never touched during optimization. \\\\\nMeta-learner & The second-level model in a stacking ensemble that is trained on the out-of-fold predictions of base learners and learns the optimal combination of their outputs. \\\\\nOOF (out-of-fold) predictions & Predictions on held-out inner validation folds; every training example receives a prediction from a model that was never fitted on it. \\\\\nKAN-Bag & The seed-bagged Chebyshev-polynomial KAN classifier proposed in this study. \\\\\nKASTLE-X & The full stacking ensemble combining KAN-Bag with seven conventional Bayesian-optimized learners. \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\n\\subsection{Dataset and Preprocessing}\n\nThe IBM HR Analytics Employee Attrition \\& Performance dataset \\citep{ibm_dataset} contains 1{,}470 employee records with 35 attributes. The binary target \\textsc{Attrition} takes value \\textit{Yes} for 237 records (16.12\\%) and \\textit{No} for 1{,}233 records (83.88\\%), yielding an imbalance ratio of approximately $5.2{:}1$. The dataset has zero missing values and zero duplicated rows. Four non-informative constant columns (\\textsc{EmployeeCount}, \\textsc{Over18}, \\textsc{StandardHours}, \\textsc{EmployeeNumber}) were removed, leaving 30 raw attributes spanning five conceptual domains: (a) demographics, (b) compensation and incentives, (c) job context, (d) attitudinal Likert scales, and (e) tenure history. Seven categorical features were one-hot encoded without reference-category dropping, producing a 51-feature matrix from raw attributes. Models requiring standardized inputs (logistic regression, SVM, KAN) applied a \\textsc{StandardScaler} fitted exclusively on the training partition of each fold.\n\n\\textbf{Important contextual note.} The IBM HR Analytics dataset is a synthetic release used widely as a benchmark. The present study treats it as such: all findings are bounds on a single synthetic benchmark, and generalization to other organizations requires external validation.\n\n\\subsection{Leakage-Free Feature Engineering}\n\nTwelve domain-motivated engineered features were constructed as strictly row-wise transformations, using only the individual row's attributes and universal constants. This makes data leakage structurally impossible: the same mapping applies to any training or test partition. Let $\\text{OT}=\\mathbb{1}\\{\\textsc{OverTime}=\\textit{Yes}\\}$ and $\\varepsilon=10^{-6}$. Intuitively, these features encode quantities that standard employee records capture indirectly: for instance, $f_1$ measures income adequacy relative to job level (detecting undercompensation), $f_5$ measures career stagnation, and $f_{10}$ captures the interaction of overtime demand with work--life balance (an overtime stress signal). Such constructions reflect the job-demands--resources model from organizational psychology.\n\n\\begin{align}\nf_1 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{JobLevel}+\\varepsilon}, &\nf_2 &= \\frac{\\textsc{MonthlyIncome}}{\\textsc{Age}+\\varepsilon}, &\nf_3 &= \\frac{\\textsc{YearsAtCompany}}{\\textsc{TotalWorkingYears}+1} \\label{eq:fe1}\\\\\nf_4 &= \\frac{\\textsc{TotalWorkingYears}}{\\textsc{NumCompaniesWorked}+1}, &\nf_5 &= \\frac{\\textsc{YearsSinceLastPromotion}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe2}\\\\\nf_6 &= \\frac{\\textsc{YearsWithCurrManager}}{\\textsc{YearsAtCompany}+1}, &\nf_7 &= \\frac{\\textsc{YearsInCurrentRole}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe3}\\\\\nf_8 &= \\tfrac{1}{4}(\\textsc{JobSat}+\\textsc{EnvSat}+\\textsc{RelSat}+\\textsc{WLB}), &\nf_9 &= \\textsc{JobInvolvement}\\times\\textsc{JobSatisfaction} \\label{eq:fe4}\\\\\nf_{10} &= \\text{OT}\\times(5-\\textsc{WLB}), &\nf_{11} &= \\textsc{DistanceFromHome}\\times\\text{OT}, &\nf_{12} &= \\frac{\\textsc{PercentSalaryHike}}{\\textsc{YearsAtCompany}+1} \\label{eq:fe5}\n\\end{align}\n\nTogether with the 51 raw encoded features, the final design matrix is $\\mathbf{X}\\in\\mathbb{R}^{1470\\times 63}$.\n\n\\subsection{Component Contribution Ablation}\n\nTo isolate the contributions of the KAN architecture, seed bagging, Bayesian optimization, and feature engineering---as requested by Reviewer 3---we conducted a four-condition ablation on a fixed 5-fold stratified CV (Table~\\ref{tab:ablation_components}). Condition A uses raw (non-engineered) features, a single-seed KAN-Net without bagging, and no Bayesian optimization. Each subsequent condition adds one component. This design supports attributing performance increments to specific methodological choices rather than to the composite package.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Component contribution ablation ($5$-fold stratified CV, mean $\\pm$ std on AUC). Each row adds one component to the prior row to isolate its contribution.}\\label{tab:ablation_components}\n\\begin{tabular}{llccc}\n\\toprule\n\\textbf{Condition} & \\textbf{Components Active} & \\textbf{AUC} & \\textbf{F1} & $\\boldsymbol{\\Delta}$ \\textbf{AUC vs.\\ A} \\\\\n\\midrule\nA & Raw features, single-seed KAN-Net & $0.7931 \\pm 0.031$ & $0.4853$ & --- \\\\\nB & + Engineered features ($f_1$--$f_{12}$) & $0.8227 \\pm 0.016$ & $0.5426$ & $+0.0296$ \\\\\nC & + Seed bagging ($S=3$, no BO) & $0.8391 \\pm 0.022$ & $0.5712$ & $+0.0460$ \\\\\nD & + Bayesian hyperparameter optimization & $0.8485 \\pm 0.027$ & $0.5945$ & $+0.0554$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nThe ablation shows that feature engineering contributes $+0.030$ AUC, seed bagging a further $+0.016$, and Bayesian optimization a further $+0.009$. These increments are additive and independently meaningful. The KAN architecture itself is best assessed by comparing Condition A against the analogous MLP-based condition (Table~\\ref{tab:zoo}), where KAN-Net (single seed) outperforms the MLP by $0.0394$ AUC on the same engineered features.\n\n\\subsection{Chebyshev-KAN Tabular Classifier}\n\n\\subsubsection{Architecture}\n\nThe Kolmogorov--Arnold representation theorem \\citep{kolmogorov_1957} states that any continuous $f:[0,1]^n\\to\\mathbb{R}$ admits\n\\begin{equation}\\label{eq:ka_theorem}\nf(x_1,\\ldots,x_n) = \\sum_{q=0}^{2n} \\Phi_q\\!\\left(\\sum_{p=1}^{n}\\varphi_{q,p}(x_p)\\right)\n\\end{equation}\nfor continuous univariate functions $\\varphi_{q,p}$ and $\\Phi_q$. Intuitively, this guarantees that the network can, in principle, represent complex nonlinear interactions between employee features and attrition risk without requiring an exponentially growing number of parameters.\n\nMotivated by~\\eqref{eq:ka_theorem}, an $L$-layer KAN with width vector $[n_0,\\ldots,n_L]$ applies at each layer $\\ell$ a learnable univariate edge function $\\varphi_{\\ell,j,i}$ to each input coordinate $x_{\\ell,i}$ and sums:\n\\begin{equation}\\label{eq:kan_layer}\nx_{\\ell+1,j} = \\sum_{i=1}^{n_\\ell} \\varphi_{\\ell,j,i}(x_{\\ell,i}), \\quad j=1,\\ldots,n_{\\ell+1}.\n\\end{equation}\n\nWe parameterize each edge function using a Chebyshev polynomial basis of degree $D$. The Chebyshev polynomials $T_0,T_1,\\ldots,T_D$ satisfy the three-term recurrence\n\\begin{equation}\\label{eq:cheby_rec}\nT_0(u)=1,\\quad T_1(u)=u,\\quad T_k(u) = 2u\\,T_{k-1}(u) - T_{k-2}(u),\n\\end{equation}\nwhich admits stable batched computation. To ensure inputs lie in $[-1,1]$ (the polynomial's natural domain), a $\\tanh$ squashing is applied before basis expansion. Intuitively, this allows the network to model monotone and non-monotone response curves (e.g., the U-shaped relationship between tenure and attrition risk) through a small number of low-degree coefficients, which standard ReLU networks would require many hidden units to approximate.\n\nA ChebyKAN layer with input dimension $d_\\text{in}$, output dimension $d_\\text{out}$, and degree $D$ maintains a coefficient tensor $\\mathbf{C}\\in\\mathbb{R}^{d_\\text{in}\\times d_\\text{out}\\times(D+1)}$:\n\\begin{equation}\\label{eq:chebykan}\n\\text{out}_{j} = \\sum_{i=1}^{d_\\text{in}} \\sum_{k=0}^{D} \\mathbf{C}_{i,j,k}\\, T_k\\!\\big(\\tanh(x_i)\\big),\n\\end{equation}\nimplemented as a single \\textsc{einsum} contraction. The KAN-Net classifier is a two-layer ChebyKAN network:\n\\begin{equation}\\label{eq:kannet}\n\\mathbf{h} = \\text{LayerNorm}\\big(\\text{ChebyKAN}_{63\\to 24,D=3}(\\mathbf{x})\\big), \\quad \\hat{y} = \\sigma\\big(\\text{ChebyKAN}_{24\\to 1,D=3}(\\mathbf{h})\\big),\n\\end{equation}\nwith total parameter count $63\\cdot 24\\cdot 4 + 24\\cdot 1\\cdot 4 = 6{,}240$ trainable weights (excluding layer-norm), roughly half the comparable MLP ($64\\to 32\\to 1$, $\\approx 11{,}300$ parameters).\n\n\\subsubsection{Training Objective}\n\nGiven $N$ training examples with labels $y_i\\in\\{0,1\\}$ and class-imbalance ratio $r=N_-/N_+$, we minimize the class-weighted binary cross-entropy:\n\\begin{equation}\\label{eq:bce}\n\\mathcal{L} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{y}_i + (1-y_i)\\log(1-\\hat{y}_i)\\right],\\quad w_i = \\begin{cases} r & y_i=1 \\\\ 1 & y_i=0 \\end{cases}\n\\end{equation}\nFor the IBM benchmark $r\\approx 5.2$, upweighting minority-class contributions. Parameters are updated with Adam \\citep{kingma_adam} ($\\eta=5\\times 10^{-3}$, $L_2$ decay $\\lambda=10^{-3}$), full-batch for up to 600 epochs with early stopping on a stratified 20\\% internal validation split (patience 50 epochs, minimum improvement $10^{-4}$ AUC).\n\n\\subsubsection{Seed Bagging (KAN-Bag)}\n\nA single KAN-Net exhibited nontrivial initialization-dependent variance. KAN-Bag averages probabilities from $S=3$ KAN-Net instances trained with distinct seeds $s\\in\\{42,202,777\\}$:\n\\begin{equation}\\label{eq:kanbag}\n\\hat{p}_{\\text{KAN-Bag}}(\\mathbf{x}) = \\frac{1}{S}\\sum_{s=1}^{S} \\hat{y}_s(\\mathbf{x}).\n\\end{equation}\nBy the bias--variance decomposition, if $S$ models have equal bias and pairwise error correlation $\\rho$, bagged variance is $\\sigma^2/S\\cdot[1+(S-1)\\rho]$, decreasing approximately as $1/S$ for small $\\rho$. In the component ablation (Table~\\ref{tab:ablation_components}), seed bagging raised AUC from $0.8227$ to $0.8391$---a contribution comparable to feature engineering---demonstrating that initialization variance is a primary challenge for small-dataset KAN training.\n\n\\subsection{KASTLE-X: KAN-Augmented Stacking Ensemble}\n\n\\subsubsection{Base-Learner Pool}\n\nKASTLE-X maintains a pool $\\mathcal{P}$ of $K=8$ base learners: $\\mathcal{P} = \\{\\text{LightGBM}^\\star, \\text{XGBoost}^\\star, \\text{CatBoost}, \\text{HistGB}, \\text{RF}, \\text{ExtraTrees}, \\text{LR}, \\text{KAN-Bag}\\}$, where $\\star$ denotes per-fold Bayesian optimization. This spans histogram-based gradient boosting \\citep{ke_lightgbm, chen_xgboost}, ordered boosting \\citep{prokhorenkova_catboost}, variance-reduction ensembles, a linear boundary model, and the proposed KAN architecture, maximizing conditional independence of base-learner errors. An architecture diagram of the complete KASTLE-X pipeline---from raw data through feature engineering, base learners, OOF meta-features, and meta-learner---is shown in Figure~\\ref{fig:pipeline}.\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{f4992235-9dd8-4ac0-8094-9c3d78ca4a1e.png}\n\\end{center}\n\\caption{KASTLE-X architecture diagram. Raw features are combined with 12 leakage-free engineered features to form a 63-feature design matrix. In each outer fold, base learners generate out-of-fold (OOF) meta-features on the training partition; the logistic meta-learner is trained on these OOF features. At inference time all base learners are refit on the full training partition and the meta-learner combines their predictions. The KAN-Bag component is highlighted to distinguish it from the conventional learners.}\\label{fig:pipeline}\n\\end{figure}\n\n\\subsubsection{Leakage-Free Out-of-Fold Meta-Features}\n\nLet $\\mathcal{D}=\\{(\\mathbf{x}_i,y_i)\\}_{i=1}^{N}$ be the training data for a given outer fold. Partition $\\mathcal{D}$ into $K_{\\text{in}}=5$ inner folds. For each inner fold $t$ with training set $\\mathcal{D}_t^{\\text{tr}}$ and validation set $\\mathcal{D}_t^{\\text{va}}$, train each base learner $b_k$ on $\\mathcal{D}_t^{\\text{tr}}$ and predict on $\\mathcal{D}_t^{\\text{va}}$. Each training example receives a prediction from a model never fit on it, yielding the leakage-free meta-feature matrix $\\mathbf{Z}\\in\\mathbb{R}^{N\\times K}$:\n\\begin{equation}\\label{eq:oof}\nZ_{i,k} = b_k^{\\,\\backslash t(i)}(\\mathbf{x}_i), \\quad i=1,\\ldots,N,\\ k=1,\\ldots,K.\n\\end{equation}\n\n\\subsubsection{Class-Weighted Logistic Meta-Learner}\n\nThe meta-learner is a class-balanced logistic regression with $L_2$ regularization:\n\\begin{equation}\\label{eq:meta_lr}\n\\hat{p}_{\\text{meta}}(\\mathbf{z}) = \\sigma(\\mathbf{w}^\\top\\mathbf{z} + b), \\quad \\mathbf{w}\\in\\mathbb{R}^K,\\ b\\in\\mathbb{R},\n\\end{equation}\n\\begin{equation}\\label{eq:meta_loss}\n\\mathcal{L}_{\\text{meta}} = -\\frac{1}{N}\\sum_{i=1}^{N} w_i\\!\\left[y_i\\log\\hat{p}_{\\text{meta}}(\\mathbf{z}_i) + (1-y_i)\\log(1-\\hat{p}_{\\text{meta}}(\\mathbf{z}_i))\\right] + \\lambda\\lVert\\mathbf{w}\\rVert_2^2.\n\\end{equation}\nLogistic regression is chosen as the meta-learner for four reasons: (i) convexity guarantees convergence; (ii) the weight vector $\\mathbf{w}$ provides directly interpretable attribution of each base learner's marginal contribution; (iii) under super-learner theory \\citep{vanderlaan_superlearner}, a logistic meta-learner is asymptotically optimal among convex combinations for log-loss risk; and (iv) empirically, on this dataset size ($N\\approx 1{,}176$ training samples per outer fold), logistic meta-learners outperformed MLP and KAN-residual meta-learners. Note that the logistic meta-learner operates on the base learners' predicted \\emph{probabilities} rather than on original features; as such, its weight vector explains the ensemble-level combination, not feature-level influence, which is the role of the TreeSHAP analysis in Section~\\ref{sec:shap}.\n\n\\subsubsection{F1-Optimal Threshold Selection}\n\nThe default threshold $\\tau=0.5$ is inappropriate at 16\\% prevalence. For each outer fold, the threshold is selected on inner-OOF meta-predictions:\n\\begin{equation}\\label{eq:thresh}\n\\tau^* = \\argmax_{\\tau\\in(0,1)}\\ \\text{F1}\\!\\left(\\mathbf{y},\\mathbb{1}\\{\\hat{p}_{\\text{meta}}(\\mathbf{z})\\geq\\tau\\}\\right).\n\\end{equation}\nBecause $\\tau^*$ is computed entirely within the training partition, it introduces no optimistic bias.\n\n\\subsection{Hyperparameter Optimization}\n\nLightGBM and XGBoost are optimized per outer fold using Optuna's Tree-structured Parzen Estimator (TPE) \\citep{akiba_optuna}. The complete hyperparameter search spaces and final selected values are provided in Table~\\ref{tab:hyperparams}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Hyperparameter search spaces and representative final selected values for LightGBM and XGBoost (per outer fold via Optuna TPE, 25 trials, 3-fold inner CV AUC objective). All other pool members use fixed configurations listed in the Supplementary Material.}\\label{tab:hyperparams}\n\\footnotesize\n\\begin{tabular}{lllr}\n\\toprule\n\\textbf{Model} & \\textbf{Hyperparameter} & \\textbf{Search Range} & \\textbf{Typical Selected} \\\\\n\\midrule\nLightGBM & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 390 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.063 \\\\\n & \\texttt{num\\_leaves} & $[15, 63]$ (int) & 31 \\\\\n & \\texttt{min\\_child\\_samples} & $[10, 60]$ (int) & 24 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.82 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.75 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 0.48 \\\\\n\\midrule\nXGBoost & \\texttt{n\\_estimators} & $[150, 600]$ (int) & 420 \\\\\n & \\texttt{learning\\_rate} & $[0.01, 0.20]$ (log) & 0.055 \\\\\n & \\texttt{max\\_depth} & $[3, 8]$ (int) & 5 \\\\\n & \\texttt{min\\_child\\_weight} & $[1, 10]$ (int) & 3 \\\\\n & \\texttt{subsample} & $[0.60, 1.00]$ & 0.79 \\\\\n & \\texttt{colsample\\_bytree} & $[0.60, 1.00]$ & 0.71 \\\\\n & \\texttt{reg\\_lambda} & $[10^{-3}, 10]$ (log) & 1.24 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nRegarding imbalance handling: boosting models (LightGBM, XGBoost, CatBoost, HistGB) incorporate class-imbalance handling natively via their split-gain criteria (through \\texttt{scale\\_pos\\_weight} or \\texttt{class\\_weight}), and no additional resampling is applied because our ablation (Table~\\ref{tab:imbalance}) confirmed that SMOTE/ADASYN degraded AUC for GBDT learners on this dataset. For tree ensembles (RF, ExtraTrees) and logistic regression, explicit \\texttt{class\\_weight=\"balanced\"} is used. We note that no multiple-comparison correction is applied to the statistical tests in Table~\\ref{tab:stats}, as each comparison is a pre-specified pairwise test of a distinct ensemble configuration against KASTLE-X; we report raw $p$-values and encourage readers to interpret them conservatively.\n\n\\subsection{Evaluation Protocol}\n\nThe protocol is fully nested to eliminate all known leakage pathways. The outer loop uses 5-fold stratified CV (seed 42); the inner loop uses 5-fold stratified CV within each outer training partition. Within a single outer fold: (i) outer split; (ii) inner-OOF generation of $\\mathbf{Z}$; (iii) Optuna tuning on the training partition; (iv) meta-learner training on $(\\mathbf{Z},\\mathbf{y}^{\\text{tr}})$; (v) isotonic calibration on OOF predictions (calibrated variant only); (vi) $\\tau^*$ selection via~\\eqref{eq:thresh}; (vii) refit of all base learners on the full training partition; (viii) test inference; (ix) metric computation. Steps (ii)--(vi) are strictly confined to $\\mathcal{D}^{\\text{tr}}$; only step (ix) accesses $\\mathcal{D}^{\\text{te}}$.\n\nReported metrics: ROC-AUC, PR-AUC, F1, balanced accuracy, MCC, and Brier score as mean $\\pm$ std across five outer folds. Fold-wise AUC differences are assessed with the paired $t$-test and Wilcoxon signed-rank test ($n=5$; the attainable Wilcoxon minimum is $p=0.0625$).\n\n\n%===================================================================\n\\section{Results}\\label{sec:results}\n%===================================================================\n\n\\subsection{Exploratory Analysis}\n\nThe class distribution is markedly imbalanced (Figure~\\ref{fig:class}). Kernel-density comparisons show leavers concentrated at younger ages, lower incomes, and shorter tenures (Figure~\\ref{fig:kde}). Categorical breakdowns show elevated attrition among overtime workers, frequent travelers, single employees, and sales roles; ordinal engagement variables show monotone gradients where attrition declines as satisfaction and involvement increase (Figures~\\ref{fig:cat} and~\\ref{fig:ordinal}). Risk is front-loaded in the first one to three years (Figure~\\ref{fig:tenure}). Mutual-information analysis confirms that six of the twelve engineered features appear in the top-20 ranking, with \\textsc{OverTimeStress} ($f_{10}$) the second most informative feature overall (Figures~\\ref{fig:mi} and~\\ref{fig:mieng}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.5\\linewidth]{Screenshot_77.png}\n\\end{center}\n\\caption{Class distribution of the attrition label (prevalence $= 0.161$, $n=1{,}470$).}\\label{fig:class}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_78.png}\n\\end{center}\n\\caption{Kernel-density comparisons of key numeric features by attrition status.}\\label{fig:kde}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_76.png}\n\\end{center}\n\\caption{Attrition rates across categorical features.}\\label{fig:cat}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_79.png}\n\\end{center}\n\\caption{Attrition rate across ordinal engagement variables.}\\label{fig:ordinal}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.95\\linewidth]{Screenshot_75.png}\n\\end{center}\n\\caption{Attrition rate by tenure bins.}\\label{fig:tenure}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_73.png}\n\\end{center}\n\\caption{Top-20 features by mutual information, including engineered features.}\\label{fig:mi}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.75\\linewidth]{Screenshot_74.png}\n\\end{center}\n\\caption{Mutual-information ranking restricted to the twelve engineered features.}\\label{fig:mieng}\n\\end{figure}\n\n\\subsection{Imbalance-Handling Ablation}\n\nA preliminary ablation evaluated four strategies on a fixed LightGBM learner under 5-fold stratified CV (Table~\\ref{tab:imbalance}). No resampling achieved the highest AUC ($0.8125$), consistent with prior findings that SMOTE distorts GBDT decision boundaries. Main experiments therefore use no resampling for boosting models and balanced class weights for tree ensembles and logistic regression.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Imbalance-handling ablation on a fixed LightGBM learner ($5$-fold, mean $\\pm$ std). All resampling is applied strictly within training folds.}\\label{tab:imbalance}\n\\begin{tabular}{lccc}\n\\toprule\n\\textbf{Strategy} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} \\\\\n\\midrule\nNone (raw) & $0.8125 \\pm 0.023$ & $0.5639 \\pm 0.047$ & $0.4358 \\pm 0.050$ \\\\\nClass weighting (balanced) & $0.8109 \\pm 0.029$ & $0.5612 \\pm 0.055$ & $0.4547 \\pm 0.044$ \\\\\nSMOTE (within-fold) & $0.8014 \\pm 0.019$ & $0.5490 \\pm 0.052$ & $0.4350 \\pm 0.047$ \\\\\nADASYN (within-fold) & $0.8035 \\pm 0.019$ & $0.5547 \\pm 0.047$ & $0.4376 \\pm 0.033$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Individual Model Benchmark}\n\nTwenty classifiers were evaluated on the 63-feature design matrix under 5-fold stratified CV (Table~\\ref{tab:zoo}, Figure~\\ref{fig:zoo}). \\textbf{KAN-Bag achieves the highest AUC ($0.8485$), PR-AUC ($0.6354$), F1 ($0.5945$), balanced accuracy ($0.7780$), and MCC ($0.5131$) among all 20 individual classifiers.} Minority-class precision is 0.630 and minority-class recall is 0.562. The second-best on AUC is LDA ($0.8267$). All four GBDT variants are outperformed by KAN-Bag at the zoo-evaluation stage; they perform substantially better as pool members after per-fold Bayesian tuning.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Individual model benchmark on engineered features ($5$-fold, mean $\\pm$ std). Best value per metric in bold. Minority-class (attrition=Yes) Prec./Rec.\\ are for information at the F1-optimal threshold.}\\label{tab:zoo}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Model} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Min.Prec} & \\textbf{Min.Rec} \\\\\n\\midrule\n\\textbf{KAN-Bag (proposed)} & $\\mathbf{0.8485 \\pm 0.027}$ & $\\mathbf{0.6354 \\pm 0.057}$ & $\\mathbf{0.5945 \\pm 0.044}$ & $\\mathbf{0.7780 \\pm 0.020}$ & $\\mathbf{0.5131 \\pm 0.053}$ & $\\mathbf{0.630}$ & $0.562$ \\\\\nLDA & $0.8267 \\pm 0.026$ & $0.6300 \\pm 0.059$ & $0.5548 \\pm 0.076$ & $0.7126 \\pm 0.042$ & $0.5032 \\pm 0.081$ & $0.544$ & $0.566$ \\\\\nLogistic Regression & $0.8247 \\pm 0.024$ & $0.5952 \\pm 0.044$ & $0.4857 \\pm 0.015$ & $0.7400 \\pm 0.017$ & $0.3801 \\pm 0.024$ & $0.471$ & $0.501$ \\\\\nLinear SVM & $0.8235 \\pm 0.026$ & $0.6015 \\pm 0.049$ & $0.3703 \\pm 0.068$ & $0.6153 \\pm 0.027$ & $0.4007 \\pm 0.064$ & $0.641$ & $0.262$ \\\\\nRandom Forest & $0.8227 \\pm 0.041$ & $0.5775 \\pm 0.068$ & $0.4471 \\pm 0.044$ & $0.6522 \\pm 0.020$ & $0.4115 \\pm 0.063$ & $0.468$ & $0.428$ \\\\\nKAN-Net (single) & $0.8227 \\pm 0.016$ & $0.5790 \\pm 0.059$ & $0.5426 \\pm 0.061$ & $0.7508 \\pm 0.043$ & $0.4483 \\pm 0.076$ & $0.547$ & $0.539$ \\\\\nSVM (RBF) & $0.8200 \\pm 0.026$ & $0.5799 \\pm 0.039$ & $0.4797 \\pm 0.025$ & $0.6664 \\pm 0.014$ & $0.4540 \\pm 0.024$ & $0.502$ & $0.458$ \\\\\nAdaBoost & $0.8198 \\pm 0.029$ & $0.5965 \\pm 0.056$ & $0.4895 \\pm 0.057$ & $0.6733 \\pm 0.026$ & $0.4494 \\pm 0.073$ & $0.491$ & $0.489$ \\\\\nExtra Trees & $0.8146 \\pm 0.025$ & $0.5729 \\pm 0.066$ & $0.5063 \\pm 0.051$ & $0.6903 \\pm 0.021$ & $0.4366 \\pm 0.074$ & $0.508$ & $0.504$ \\\\\nCatBoost & $0.8115 \\pm 0.026$ & $0.5934 \\pm 0.037$ & $0.4262 \\pm 0.051$ & $0.6409 \\pm 0.024$ & $0.4160 \\pm 0.041$ & $0.434$ & $0.419$ \\\\\nBagging (DT) & $0.8039 \\pm 0.031$ & $0.5431 \\pm 0.034$ & $0.4362 \\pm 0.051$ & $0.6470 \\pm 0.023$ & $0.3990 \\pm 0.071$ & $0.440$ & $0.433$ \\\\\nHistGB & $0.8035 \\pm 0.025$ & $0.5507 \\pm 0.048$ & $0.4286 \\pm 0.047$ & $0.6435 \\pm 0.024$ & $0.4013 \\pm 0.035$ & $0.435$ & $0.423$ \\\\\nGradient Boosting & $0.8029 \\pm 0.016$ & $0.5528 \\pm 0.015$ & $0.4372 \\pm 0.060$ & $0.6509 \\pm 0.031$ & $0.3918 \\pm 0.045$ & $0.439$ & $0.435$ \\\\\nLightGBM & $0.8022 \\pm 0.036$ & $0.5521 \\pm 0.048$ & $0.4227 \\pm 0.064$ & $0.6414 \\pm 0.030$ & $0.3980 \\pm 0.050$ & $0.425$ & $0.420$ \\\\\nXGBoost & $0.7999 \\pm 0.026$ & $0.5570 \\pm 0.042$ & $0.4211 \\pm 0.039$ & $0.6390 \\pm 0.016$ & $0.3962 \\pm 0.062$ & $0.423$ & $0.419$ \\\\\nGaussian NB & $0.7841 \\pm 0.041$ & $0.4775 \\pm 0.037$ & $0.4562 \\pm 0.024$ & $0.7226 \\pm 0.022$ & $0.3431 \\pm 0.035$ & $0.349$ & $0.659$ \\\\\nMLP & $0.7833 \\pm 0.042$ & $0.5438 \\pm 0.057$ & $0.4591 \\pm 0.053$ & $0.6695 \\pm 0.028$ & $0.3717 \\pm 0.062$ & $0.460$ & $0.459$ \\\\\nKNN & $0.7775 \\pm 0.044$ & $0.4681 \\pm 0.060$ & $0.1874 \\pm 0.048$ & $0.5515 \\pm 0.014$ & $0.2768 \\pm 0.037$ & $0.387$ & $0.120$ \\\\\nQDA & $0.7516 \\pm 0.035$ & $0.4326 \\pm 0.056$ & $0.4524 \\pm 0.019$ & $0.6923 \\pm 0.016$ & $0.3320 \\pm 0.025$ & $0.345$ & $0.662$ \\\\\nDecision Tree & $0.6666 \\pm 0.038$ & $0.3498 \\pm 0.020$ & $0.4154 \\pm 0.033$ & $0.6697 \\pm 0.027$ & $0.2825 \\pm 0.045$ & $0.409$ & $0.422$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.8\\linewidth]{Screenshot_72.png}\n\\end{center}\n\\caption{Individual model benchmark ($5$-fold stratified CV). KAN-Bag attains the highest AUC among all twenty individual classifiers.}\\label{fig:zoo}\n\\end{figure}\n\n\\subsection{Ensemble Comparison}\n\nNested-CV results for six ensemble variants are presented in Table~\\ref{tab:ensembles}. KASTLE-X achieves AUC $0.8449\\pm0.020$, PR-AUC $0.6570\\pm0.051$, and F1 $0.5831\\pm0.035$. Minority-class recall is 59.5\\% and minority-class precision is 62.4\\%.\n\n\\textbf{Reframing KASTLE-X's contribution (per Reviewer 2).} KAN-Bag is the strongest individual classifier, and KASTLE-X does not surpass KAN-Bag on AUC ($0.8449$ vs.\\ $0.8485$). The contribution of KASTLE-X lies elsewhere: the ensemble improves over the non-KAN stacking baseline (Stacking-LR no KAN, $0.8335$ AUC) by $+0.0114$ AUC and $+0.0698$ F1, and it achieves this consistently on all five outer folds. KASTLE-X should therefore be understood not as a universally superior predictor, but as evidence that \\emph{KAN augmentation within stacking provides incremental value beyond a conventional pool of seven learners}. Whether a practitioner prefers KAN-Bag (simpler, slightly higher AUC) or KASTLE-X (higher F1, better PR-AUC) depends on the operational cost structure.\n\n\\begin{table}[h!]\n\\centering\n\\caption{KASTLE-X ensemble comparison, nested $5$-fold CV (mean $\\pm$ std). Model complexity is shown as approximate total parameter count / training time relative to Stacking-LR (no KAN).}\\label{tab:ensembles}\n\\footnotesize\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Method} & \\textbf{AUC} & \\textbf{PR-AUC} & \\textbf{F1} & \\textbf{BalAcc} & \\textbf{MCC} & \\textbf{Brier} & \\textbf{Rel.\\,Time} \\\\\n\\midrule\n\\textbf{KASTLE-X (proposed)} & $\\mathbf{0.8449 \\pm 0.020}$ & $\\mathbf{0.6570 \\pm 0.051}$ & $\\mathbf{0.5831 \\pm 0.035}$ & $0.7574 \\pm 0.030$ & $\\mathbf{0.5054 \\pm 0.036}$ & $0.1424 \\pm 0.021$ & $1.0\\times$ \\\\\nKASTLE-X + isotonic & $0.8410 \\pm 0.021$ & $0.6276 \\pm 0.056$ & $0.5831 \\pm 0.035$ & $0.7574 \\pm 0.030$ & $0.5054 \\pm 0.036$ & $\\mathbf{0.0918 \\pm 0.010}$ & $1.0\\times$ \\\\\nKASTLE-X KANres meta & $0.8422 \\pm 0.026$ & $0.6543 \\pm 0.049$ & $0.5665 \\pm 0.058$ & $0.7483 \\pm 0.041$ & $0.4865 \\pm 0.063$ & $0.1414 \\pm 0.029$ & $1.1\\times$ \\\\\nRank-average voting & $0.8388 \\pm 0.025$ & $0.6382 \\pm 0.061$ & $0.5665 \\pm 0.043$ & $0.7452 \\pm 0.034$ & $0.4844 \\pm 0.049$ & $0.2344 \\pm 0.007$ & $0.9\\times$ \\\\\nSoft voting & $0.8404 \\pm 0.023$ & $0.6338 \\pm 0.058$ & $0.5215 \\pm 0.025$ & $0.6918 \\pm 0.012$ & $0.4764 \\pm 0.048$ & $0.0956 \\pm 0.008$ & $0.9\\times$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $0.8335 \\pm 0.021$ & $0.6382 \\pm 0.055$ & $0.5133 \\pm 0.032$ & $\\mathbf{0.7541 \\pm 0.026}$ & $0.4135 \\pm 0.044$ & $0.1550 \\pm 0.012$ & $0.7\\times$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_71.png}\n\\end{center}\n\\caption{ROC curves for KASTLE-X and comparison ensembles on pooled OOF predictions.}\\label{fig:roc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_70.png}\n\\end{center}\n\\caption{Precision--recall curves; dashed line marks the prevalence baseline (0.161).}\\label{fig:pr}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_69.png}\n\\end{center}\n\\caption{Fold-wise AUC across five outer folds. KASTLE-X exceeds Stacking-LR (no KAN) on every fold.}\\label{fig:foldauc}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.65\\linewidth]{Screenshot_68.png}\n\\end{center}\n\\caption{Ensemble learning curve (diagnostic). Validation AUC continues to improve modestly with additional training examples, indicating performance is not saturated at $n=1{,}470$.}\\label{fig:learning}\n\\end{figure}\n\n\\subsection{Ablation and Statistical Tests}\n\n\\subsubsection{KAN Augmentation Ablation}\n\nKASTLE-X vs.\\ Stacking-LR (no KAN) on fold-wise AUC:\n\n\\begin{center}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Fold} & \\textbf{KASTLE-X} & \\textbf{Stacking-LR (no KAN)} \\\\\n\\midrule\n1 & 0.8327 & 0.8277 ($+0.0050$) \\\\\n2 & 0.8356 & 0.8209 ($+0.0147$) \\\\\n3 & 0.8746 & 0.8642 ($+0.0104$) \\\\\n4 & 0.8567 & 0.8451 ($+0.0116$) \\\\\n5 & 0.8251 & 0.8097 ($+0.0154$) \\\\\n\\midrule\nMean $\\pm$ SD & $0.8449\\pm0.020$ & $0.8335\\pm0.021$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{center}\n\nThe AUC difference is positive on every fold; paired $t(4)=5.85$, $p=0.0036$ (95\\% CI for $\\Delta$AUC: $[0.0057,\\ 0.0172]$). The Wilcoxon signed-rank test yields $p=0.0625$ (minimum attainable with $n=5$ pairs). The discrepancy between the two tests is expected: with only five pairs, the paired $t$-test leverages the magnitude of differences whereas the Wilcoxon test uses only signs; both are consistent with a real but small effect, and inferential claims are explicitly qualified by $n=5$ in this paper.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Fold-wise statistical comparison ($n=5$ folds). Paired $t$-test and Wilcoxon signed-rank $p$-values on AUC. 95\\% confidence intervals for mean fold-wise $\\Delta$AUC are shown.}\\label{tab:stats}\n\\begin{tabular}{lcccc}\n\\toprule\n\\textbf{Comparison (KASTLE-X vs.)} & $\\boldsymbol{\\Delta}$\\textbf{AUC} & \\textbf{95\\% CI} & \\textbf{Paired $t$ $p$} & \\textbf{Wilcoxon $p$} \\\\\n\\midrule\nKASTLE-X + isotonic & $+0.0039$ & $[0.0028,\\ 0.0049]$ & $0.0001$ & $0.0625$ \\\\\nKASTLE-X KANres meta & $+0.0027$ & $[-0.0073,\\ 0.0127]$ & $0.5517$ & $1.0000$ \\\\\n\\textbf{Stacking-LR (no KAN)} & $\\mathbf{+0.0114}$ & $\\mathbf{[0.0057,\\ 0.0172]}$ & $\\mathbf{0.0036}$ & $\\mathbf{0.0625}$ \\\\\nSoft voting & $+0.0045$ & $[0.0009,\\ 0.0082]$ & $0.0239$ & $0.0625$ \\\\\nRank-average voting & $+0.0061$ & $[-0.0035,\\ 0.0157]$ & $0.1619$ & $0.1875$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsubsection{Statistical Justification for the AUC Gain (Reviewer 3)}\n\nReviewer 3 raises the question of whether a $0.0114$ AUC gain is meaningful given only 237 positive observations. We address this at two levels. (1) \\emph{Statistical level}: the paired $t$-test detects a consistent within-fold improvement ($p=0.0036$) that is not attributable to sampling noise across folds; the 95\\% CI $[0.0057,\\ 0.0172]$ excludes zero. (2) \\emph{Practical level}: operationally, the F1 gain of $+0.0698$ translates directly to more correct attrition identifications per screening cycle. At the F1-optimal threshold, KASTLE-X correctly identifies 141 true positives compared with $\\approx 124$ for Stacking-LR (no KAN)---17 additional employees correctly flagged per full-workforce screening, reducing downstream replacement costs. We emphasize that these figures are illustrative for a synthetic benchmark and are not an organizational deployment study.\n\n\\subsection{Pooled Out-of-Fold Analysis}\n\nOn pooled OOF predictions (all 1{,}470 examples evaluated exactly once), KASTLE-X achieves AUC $=0.8404$, PR-AUC $=0.6432$, and at $\\tau^*=0.716$, F1 $=0.6091$. Confusion matrix: $[[1148,\\ 85],\\ [96,\\ 141]]$ (stayers/leavers predicted correctly on the diagonal). This yields sensitivity $=59.49\\%$, specificity $=93.11\\%$, precision $=62.39\\%$, false-positive rate $=6.89\\%$.\n\n\\textbf{Business translation (illustrative, synthetic benchmark).} A monthly screening of the full workforce would flag 226 employees (15.4\\%), of whom 141 are genuine attrition risks---a $3.7\\times$ enrichment over the 16.1\\% base attrition rate. At the F1-optimal threshold, the model would identify approximately 3 out of every 5 at-risk employees for proactive intervention. These figures are explicitly illustrative and should not be interpreted as deployment-ready estimates for any real organization, as the underlying dataset is synthetic.\n\n\\subsection{Meta-Learner Interpretability}\n\nThe logistic meta-learner coefficients trained on all 1{,}470 pooled OOF predictions provide a direct measure of each base learner's marginal contribution to the ensemble (Table~\\ref{tab:meta}). KAN-Bag receives the largest positive coefficient ($+2.5052$), followed by random forest ($+1.3778$) and logistic regression ($+1.1095$). The negative coefficients for LightGBM and HistGB reflect redundancy with other pool members, not individual harmfulness. The pool's prediction correlation matrix confirms KAN-Bag has the lowest average pairwise correlation with remaining pool members (Figure~\\ref{fig:pooldiv}), validating the architectural diversity argument.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Meta-learner coefficients from the logistic regression trained on all 1{,}470 pooled OOF predictions. A positive coefficient indicates a net positive marginal contribution; negative coefficients reflect redundancy with higher-weighted pool members.}\\label{tab:meta}\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Base Learner} & \\textbf{Meta Coefficient} & \\textbf{Interpretation} \\\\\n\\midrule\nKAN-Bag & $+2.5052$ & Largest marginal contribution; architecturally distinct \\\\\nRandom Forest & $+1.3778$ & Strong independent variance reduction \\\\\nLogistic Regression & $+1.1095$ & Orthogonal linear signal \\\\\nCatBoost & $+0.7608$ & Distinct ordered-boosting signal \\\\\nXGBoost & $+0.5165$ & Moderate incremental value \\\\\nExtra Trees & $+0.2423$ & Small but positive incremental gain \\\\\nHistGB & $-0.1212$ & Redundant with LightGBM/XGBoost \\\\\nLightGBM & $-0.3363$ & Redundant with XGBoost/HistGB \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_67.png}\n\\end{center}\n\\caption{Pool prediction-correlation matrix. KAN-Bag has the lowest average pairwise correlation with remaining pool members, supporting the architectural diversity argument.}\\label{fig:pooldiv}\n\\end{figure}\n\n\\subsection{SHAP Interpretability}\\label{sec:shap}\n\nTreeSHAP was applied to the Optuna-tuned LightGBM learner (Figures~\\ref{fig:beeswarm} and~\\ref{fig:shapimp}). We note explicitly (per Reviewer 2) that this SHAP analysis explains the LightGBM \\emph{component} of KASTLE-X, not the full ensemble; it is positioned as component-level evidence for feature importance rather than ensemble-level attribution. The meta-learner coefficients (Table~\\ref{tab:meta}) and the prediction-diversity matrix (Figure~\\ref{fig:pooldiv}) provide the ensemble-level view.\n\nThe five most influential features are \\textsc{OverTime\\_Yes}, \\textsc{OverTimeStress} ($f_{10}$, engineered), \\textsc{MonthlyIncome}, \\textsc{IncomePerLevel} ($f_1$, engineered), and \\textsc{TotalWorkingYears}. Overtime exerts the largest single effect. The engineered $f_{10}$ provides complementary dose--response information beyond the binary indicator. Income features show a strong monotone negative relationship with attrition. These patterns are consistent across income, role, and tenure dimensions (Figures~\\ref{fig:dep_income}--\\ref{fig:dep_joblevel}).\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_66.png}\n\\end{center}\n\\caption{SHAP beeswarm summary for the tuned LightGBM component (not the full KASTLE-X ensemble). This analysis provides component-level feature attribution.}\\label{fig:beeswarm}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.7\\linewidth]{Screenshot_65.png}\n\\end{center}\n\\caption{Mean absolute SHAP feature importance for the tuned LightGBM component.}\\label{fig:shapimp}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_61.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{MonthlyIncome}, coloured by overtime status.}\\label{fig:dep_income}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_63.png}\n\\end{center}\n\\caption{SHAP dependence plot for engineered \\textsc{IncomePerLevel} ($f_1$).}\\label{fig:dep_ipl}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_62.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{YearsAtCompany}, showing front-loaded early-tenure attrition risk.}\\label{fig:dep_years}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=0.6\\linewidth]{Screenshot_64.png}\n\\end{center}\n\\caption{SHAP dependence plot for \\textsc{JobLevel}, showing monotone decrease in attrition contribution with seniority.}\\label{fig:dep_joblevel}\n\\end{figure}\n\n\n%===================================================================\n\\section{Discussion}\\label{sec:discussion}\n%===================================================================\n\n\\subsection{Theoretical Significance}\n\nThis study contributes to two theoretical streams. First, it provides direct empirical evidence that KANs---whose learnable polynomial edge functions can represent monotone and non-monotone response curves flexibly---are architecturally distinctive from GBDTs on small-scale, noisy HR tabular data. Specifically, KAN-Bag achieves higher AUC than all four GBDT variants at the zoo benchmark stage, a result consistent with the hypothesis that the attitudinal Likert features in this dataset have response relationships better captured by polynomial bases than by axis-aligned splits. Second, the KAN-augmented stacking result confirms ensemble diversity theory \\citep{kuncheva_whitaker}: when a new learner's error correlations with an existing pool are lower than the pool's internal correlations, adding it improves the ensemble even when its standalone AUC is not highest, because the meta-learner can exploit its residual information.\n\n\\subsection{Empirical Contributions}\n\nThis study provides the most complete honest evaluation of the IBM HR attrition benchmark to date: 20 individual models, 6 ensemble variants, 7 performance metrics, formal statistical tests with confidence intervals, calibration analysis, and component ablation, all under a protocol that eliminates leakage. The comparison with published prior work on the same dataset, summarized in Table~\\ref{tab:prior}, illustrates the evaluation-protocol dependence of reported performance: studies using pre-split SMOTE report F1 values 25--50 percentage points above our honest estimates, confirming the data-leakage hypothesis of \\citet{rahman_review}.\n\n\\begin{table}[h!]\n\\centering\n\\caption{Comparison with published results on the IBM HR Analytics benchmark. Studies are ordered by reported AUC. All our results are from the current honest nested-CV evaluation. The protocol column flags the primary methodological concern.}\\label{tab:prior}\n\\footnotesize\n\\begin{tabular}{lcccp{4.2cm}}\n\\toprule\n\\textbf{Study} & \\textbf{Best Model} & \\textbf{Reported AUC} & \\textbf{Reported F1} & \\textbf{Evaluation Protocol} \\\\\n\\midrule\n\\citet{bibliometric_attrition_2025} & Ensemble & $\\sim$0.90 & $\\sim$0.88 & Pre-split SMOTE (leakage likely) \\\\\n\\citet{slr_attrition_2024} & XGBoost & $\\sim$0.87 & $\\sim$0.83 & Hold-out; pre-split oversampling \\\\\n\\citet{alqarni_power_bi_2025} & RF + BI & $\\sim$0.86 & $\\sim$0.81 & Single split; pre-split SMOTE \\\\\n\\textbf{This study} (KASTLE-X) & Stacking & $0.8449$ & $0.5831$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\textbf{This study} (KAN-Bag) & Individual & $0.8485$ & $0.5945$ & Nested 5$\\times$5-fold, no leakage \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Practical Implications}\n\nFor HR analytics practitioners, the results have several actionable implications. First, the $3.7\\times$ enrichment of the KASTLE-X screening list over the base attrition rate means that a limited number of HR interventions can be directed at the highest-risk employees, substantially improving the cost-effectiveness of retention programs. Second, the SHAP analysis identifies overtime load, income adequacy, and early tenure as the three primary attrition drivers in this benchmark; targeted interventions addressing these factors (flexible work arrangements, transparent compensation benchmarking, structured onboarding programs) may be more effective than generic engagement programs. Third, practitioners should select the decision threshold $\\tau^*$ based on the asymmetric costs of false positives (unnecessary retention spending) and false negatives (missed departures) in their organizational context, rather than using the default 0.5. Fourth, we emphasize that KASTLE-X is a predictive association model, not a causal intervention model: finding that overtime predicts attrition does not by itself prove that reducing overtime would reduce attrition, and causal claims require randomized field experiments.\n\n\\subsection{Research Limitations}\n\n\\textbf{Single-dataset scope.} The study uses one benchmark dataset representing one organization in a synthetic release. All performance figures are bounds on this specific benchmark; generalization to other organizational contexts, industries, or cultures requires external validation. In the absence of a second public HR attrition dataset with equivalent attributes, we clearly position this as a single-dataset limitation central to the conclusion.\n\n\\textbf{Statistical power.} Five outer folds limits the Wilcoxon test to its minimum $p=0.0625$. The paired $t$-test provides more power under the normality assumption but is sensitive to that assumption with $n=5$. Replication with ten-fold outer CV would provide more reliable inferences.\n\n\\textbf{Dataset size.} With 237 positive cases, the standard error on minority-class metrics is substantial. The component ablation results and fold-wise AUC differences are consistent but should be interpreted with this in mind.\n\n\\textbf{SHAP scope.} The SHAP analysis explains the LightGBM component, not the full ensemble. Full-ensemble attributions would require model-agnostic methods (e.g., LIME or Kernel SHAP) applied to the meta-learner output, which is a direction for future work.\n\n\\textbf{Causal interpretation.} Predictive associations identified by SHAP do not imply causal effects. The claim that overtime load predicts attrition is a predictive association, not evidence that reducing overtime would reduce attrition.\n\n\\subsection{Ethical Considerations and Responsible Deployment}\n\nAutomated attrition prediction tools carry several ethical risks that practitioners must address before deployment. First, even a well-calibrated model will produce false positives---employees flagged as at-risk who are not. If such flags influence managerial behavior (differential treatment, reduced promotion consideration), they may create self-fulfilling prophecies or constitute indirect discrimination. Second, the SHAP analysis shows that age and income are among the top predictors; if these are correlated with protected characteristics in a particular organization, the model may produce disparate-impact screening. Third, employees should be informed that such tools are in use and should have recourse to challenge model-generated assessments.\n\nSHAP-based explainability, as demonstrated in this paper, is a necessary but not sufficient mitigation: it enables identification of which features drive predictions, but does not verify that the model is fair across demographic subgroups, and does not substitute for organizational governance. We recommend that any deployment of systems like KASTLE-X include: (a) a fairness audit across age, gender, and ethnicity subgroups; (b) transparency with affected employees; (c) human oversight for any consequential decisions; and (d) regular re-evaluation as workforce composition and organizational context change.\n\n\\subsection{Future Research Directions}\n\n\\textbf{External validation.} The most important next step is evaluating KASTLE-X on additional organizational attrition datasets. We are not aware of a second public dataset with equivalent attribute richness for direct comparison; constructing or obtaining such a dataset is a valuable research contribution in itself.\n\n\\textbf{Full-ensemble interpretability.} Developing model-agnostic ensemble SHAP attributions that reflect the combined meta-learner output would align interpretability with the model actually deployed.\n\n\\textbf{Larger KAN pools.} As KAN research matures and computational costs decrease, adding multiple KAN variants (wavelet KAN, B-spline KAN) to the stacking pool may further increase diversity.\n\n\\textbf{Longitudinal validation.} A prospective validation study in which model-flagged employees are tracked over time would allow calibration of confidence intervals on the business-impact figures and provide causal evidence if combined with randomized retention interventions.\n\n\\textbf{Fairness-aware variants.} Adapting KASTLE-X with fairness constraints \\citep{lundberg_shap} on demographic parity or equalized odds would extend its applicability to contexts with stringent anti-discrimination requirements.\n\n\n%===================================================================\n\\section{Conclusion}\\label{sec:conclusion}\n%===================================================================\n\nThis paper presented KASTLE-X, a KAN-augmented stacking ensemble for employee attrition prediction. The primary contribution is a rigorous test of the hypothesis that an architecturally distinct KAN component---specifically KAN-Bag, a seed-bagged Chebyshev-polynomial KAN---provides incremental value within a heterogeneous stacking ensemble. The answer, clearly bounded to this single synthetic benchmark, is yes: KASTLE-X outperforms the identically structured non-KAN stacking ensemble on all five outer folds ($p=0.0036$; $\\Delta$AUC $=+0.0114$, 95\\% CI $[0.0057,\\ 0.0172]$; $\\Delta$F1 $=+0.0698$). The logistic meta-learner assigns KAN-Bag the largest coefficient ($2.51$), and the prediction-diversity analysis confirms that KAN-Bag's error correlations with the GBDT cluster are substantially lower than intra-GBDT correlations.\n\nThe narrower claim---that KAN augmentation within stacking \\emph{may} benefit tabular ensembles under class imbalance---is better grounded and more scientifically defensible than any claim of universal superiority. KAN-Bag is also the strongest of 20 individually benchmarked classifiers (AUC $0.8485$), outperforming CatBoost, XGBoost, LDA, and all other individual models. Twelve leakage-free engineered features confirmed by mutual-information analysis and SHAP interpretability (at the component level) add measurable informativeness. A component ablation isolates the contributions of feature engineering ($+0.030$ AUC), seed bagging ($+0.016$), and Bayesian optimization ($+0.009$).\n\nThe broader methodological contribution is the most complete honest evaluation of the IBM HR attrition benchmark to date, covering 20 models, 6 ensemble variants, 7 metrics, component ablation, calibration, statistical tests with confidence intervals, and SHAP interpretability under a strictly leakage-free nested protocol. These results advance both the practical toolkit for HR analytics and the nascent empirical literature on KAN applications to business tabular data.\n\n\n%===================================================================\n\\section*{Conflict of Interest Statement}\n%===================================================================\nThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n\\section*{Author Contributions}\nFA conceived the study, designed the KASTLE-X framework and KAN-Bag classifier, implemented the experimental pipeline, and drafted the manuscript. SA contributed to feature engineering design, statistical analysis, and manuscript revision. TA supervised the study, contributed to interpretation and SHAP analysis, and revised the manuscript. All authors read and approved the final manuscript.\n\n\\section*{Funding}\nThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\n\n\\section*{Acknowledgments}\nThe authors thank the maintainers of the open-source scientific Python ecosystem (scikit-learn, LightGBM, XGBoost, CatBoost, PyTorch, Optuna) and the three anonymous reviewers whose detailed critiques substantially improved the manuscript.\n\n\\section*{Supplemental Data}\n\\href{http://home.frontiersin.org/about/author-guidelines#SupplementaryMaterial}{Supplementary Material} accompanying this article contains: (S1) complete Python implementation of the KASTLE-X pipeline; (S2) per-fold hyperparameter selections for LightGBM and XGBoost; (S3) fixed hyperparameter configurations for all other pool members; (S4) additional interpretability figures; (S5) full numerical results for all 20 individual classifiers and 6 ensemble variants.\n\n\\section*{Data Availability Statement}\nThe IBM HR Analytics Employee Attrition \\& Performance dataset is publicly available at \\url{https://www.kaggle.com/datasets/pavansubhasht/ibm-hr-analytics-attrition-dataset}. All code required to reproduce the reported results is provided as supplementary material.\n\n\\bibliographystyle{Frontiers-Harvard}\n\\bibliography{test_revised}\n\n\\end{document}",
      "tex_filename": "frontiers.tex",
      "bib_content": "@article{Paul2026,\n  title={KASTLE-X: Incremental Value of Kolmogorov\u2013Arnold Network Augmentation in a Stacked Tabular Ensemble for Employee Attrition Prediction},\n  author={Nirodh Paul and Md. Mahedi Hassan and Sumnoon Ferdous and Md. Masuqul Haque and Mir Mohammad Azad},\n  journal={Frontiers in Medicine},\n  doi={10.3389/fmed.2026.19868346},\n  year={2026}\n}\n",
      "source_dir": "/journals/medicine/articles/10.3389/fmed.2026.1986834/source",
      "tex_file": "/journals/medicine/articles/10.3389/fmed.2026.1986834/source/article.tex",
      "bib_file": "/journals/medicine/articles/10.3389/fmed.2026.1986834/source/references.bib",
      "id": "art_19868346",
      "updated_at": "2026-11-07T11:06:38Z",
      "created_at": "2026-11-07T11:06:38Z"
    },
    {
      "id": "art_7778899",
      "title": "Cutting-Edge AI in Biomedicine: Machine Learning Framework",
      "journal": "Frontiers in Artificial Intelligence",
      "journal_slug": "artificial-intelligence",
      "journal_abbrev": "Front. Artif. Intell.",
      "section": "Sec. Machine Learning and Artificial Intelligence",
      "doi": "10.3389/frai.2026.7778899",
      "article_url_path": "/journals/artificial-intelligence/articles/10.3389/frai.2026.7778899/abstract",
      "views_count": "297",
      "demographics": [
        {
          "name": "China",
          "views": 96
        },
        {
          "name": "United States",
          "views": 66
        },
        {
          "name": "Bangladesh",
          "views": 63
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        {
          "name": "India",
          "views": 40
        },
        {
          "name": "Morocco",
          "views": 32
        }
      ],
      "authors": [
        {
          "name": "Fahim Abrar",
          "affiliations": [
            "1"
          ],
          "is_corresponding": false
        },
        {
          "name": "Bentley Njie",
          "affiliations": [
            "2"
          ],
          "is_corresponding": true
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Trine University, Angola, United States"
        },
        {
          "index": "2",
          "text": "University of Washington, Seattle, United States"
        }
      ],
      "corr_author": "Bentley Njie",
      "corr_email": "bnjie@uw.edu",
      "abstract": "Artificial intelligence applications in biomedical research and translational medicine require rigorous calibration and conformal predictive assurances. This study demonstrates a multi-stage fusion architecture with leakage prevention across clinical cohorts.",
      "keywords": "Artificial Intelligence, Biomedical Informatics, Machine Learning, Clinical Decision Support",
      "impact_factor": "6.7",
      "citescore": "8.0",
      "banner": "assets/images/journals/artificial-intelligence-banner.png",
      "received": "2026-10-20",
      "accepted": "2026-11-01",
      "created_at": "2026-11-06T12:00:00Z",
      "updated_at": "2026-11-06T12:35:00Z"
    },
    {
      "title": "Regime-Aware Conformal Aggregation for Calibrated Return Intervals and Value-at-Risk in Financial Markets",
      "authors": [
        {
          "name": "Suresh Kumar Narvani",
          "affiliations": [
            "1"
          ],
          "is_corresponding": true,
          "affil_str": "1,*",
          "initials": "SN"
        },
        {
          "name": "Ipshita Kajuri",
          "affiliations": [
            "2"
          ],
          "is_corresponding": false,
          "affil_str": "2",
          "initials": "IK"
        },
        {
          "name": "Prakash Debnath",
          "affiliations": [
            "3"
          ],
          "is_corresponding": false,
          "affil_str": "3",
          "initials": "PD"
        },
        {
          "name": "Nayeem Farhan",
          "affiliations": [
            "4"
          ],
          "is_corresponding": false,
          "affil_str": "4",
          "initials": "NF"
        },
        {
          "name": "Najiba Hassan Apshora",
          "affiliations": [
            "5"
          ],
          "is_corresponding": false,
          "affil_str": "5",
          "initials": "NA"
        },
        {
          "name": "Masrufa Tasnim",
          "affiliations": [
            "6"
          ],
          "is_corresponding": false,
          "affil_str": "6",
          "initials": "MT"
        },
        {
          "name": "Rahul Rohit",
          "affiliations": [
            "7"
          ],
          "is_corresponding": false,
          "affil_str": "7",
          "initials": "RR"
        },
        {
          "name": "Sharmina Khanom",
          "affiliations": [
            "8"
          ],
          "is_corresponding": false,
          "affil_str": "8",
          "initials": "SK"
        },
        {
          "name": "Suchana Rani Roy",
          "affiliations": [
            "9"
          ],
          "is_corresponding": false,
          "affil_str": "9",
          "initials": "SR"
        },
        {
          "name": "Wawan Devis Wahyu",
          "affiliations": [
            "10"
          ],
          "is_corresponding": false,
          "affil_str": "10",
          "initials": "WW"
        }
      ],
      "affiliations": [
        {
          "index": "1",
          "text": "Department of Financial Engineering, World Quant University, Karachi, Pakistan"
        },
        {
          "index": "2",
          "text": "Department of Finance, Master of Business Administration, North South University, Dhaka, Bangladesh"
        },
        {
          "index": "3",
          "text": "Department of Finance, Master of Business Administration, North South University, Dhaka, Bangladesh"
        },
        {
          "index": "4",
          "text": "Department of Humanities and Social Sciences, Master of Science in Finance, Newcastle University, Newcastle upon Tyne, United Kingdom"
        },
        {
          "index": "5",
          "text": "Department of Pharmacy, Southeast University, Dhaka, Bangladesh"
        },
        {
          "index": "6",
          "text": "Master of Business Administration (MBA) Human Resource Management University of Dhaka"
        },
        {
          "index": "7",
          "text": "Department of Finance, Independent University Bangladesh, Dhaka, Bangladesh"
        },
        {
          "index": "8",
          "text": "Department of Economics and Banking, International Islamic University Chittagong, Chittagong, Bangladesh"
        },
        {
          "index": "9",
          "text": "Department of Economics, Comilla Government Victoria College, Comilla, Bangladesh"
        },
        {
          "index": "10",
          "text": "State Islamic Institute Kerinci, Sungai Penuh, Indonesia"
        }
      ],
      "corr_author": "Suresh Kumar Narvani",
      "corr_email": "DeaconSmawley750351@outlook.com",
      "abstract": "Machine-learning studies of financial markets often report high price-level accuracy from a single market, using point predictions without a random-walk comparison or any check that their uncertainty is reliable. We study the calibration of prediction intervals and value-at-risk (VaR) for daily returns under a leakage-controlled protocol, using 34 assets across equity indices, foreign exchange, commodities and cryptocurrencies (2000\u20132026) and a confirmation tier of 162 S&P 500 stocks. Eight quantile models, ranging from historical simulation and GJR-GARCH to LightGBM, an LSTM network and two ensembles, produced 90% intervals for one- and five-day returns. These intervals were calibrated with eleven conformal methods, including recent financial and tail-specific proposals, aggregated adaptive conformal inference (AgACI), and a new regime-aware aggregation (RA-AgCI) that learns which calibrator to trust in each real-time market regime. Evaluation used purged walk-forward cross-validation over five crisis-spanning folds, an untouched 2025\u20132026 hold-out, Holm-corrected Wilcoxon and paired t-tests, Diebold\u2013Mariano tests, the model confidence set, VaR backtests and explainable AI. Common evaluation shortcuts mattered more than any model: smoothing the series before splitting raised the out-of-sample R^2 of daily return predictions from -0.9% to 46.8%, and a random walk matched every model on price-level R^2 (0.994). No model predicted the direction of returns, but every learned model described the return distribution better than historical simulation (p<0.001), with an online quantile-weighted ensemble performing best (5.7% lower pinball loss in cross-validation and 5.2% on the hold-out). For one-day intervals, RA-AgCI gave the lowest interval score on all three base models and the highest VaR-backtest pass rates (97\u2013100% of assets), significantly improving on ACI and tail-specific ECI but not on global aggregation. Gains were below 1%, did not extend to five days, and ACI retained the smallest per-asset coverage error. On the stock tier, RA-AgCI performed best with GARCH and historical-simulation bases but not with LightGBM. Regime information is therefore most useful for models that do not adapt to volatility, and rigorous validation matters more than model choice.",
      "keywords": "uncertainty quantification, conformal prediction, value at risk, financial returns, regime shift, data leakage, model confidence set, explainable AI",
      "doi": "10.3389/frai.2026.1986834",
      "article_url_path": "/journals/artificial-intelligence/articles/10.3389/frai.2026.1986834/abstract",
      "journal_slug": "artificial-intelligence",
      "journal": "Frontiers in Artificial Intelligence",
      "journal_abbrev": "Front. Artif. Intell.",
      "section": "Sec. Medicine and Public Health",
      "banner": "/assets/images/journals/artificial-intelligence-banner.png",
      "issn": "2624-8212",
      "impact_factor": "6.7",
      "citescore": "8",
      "received": "2026-08-05",
      "accepted": "2026-10-22",
      "copyright_year": "2026",
      "article_type": "ORIGINAL RESEARCH",
      "views_count": "997",
      "demographics": [
        {
          "name": "China",
          "views": 96
        },
        {
          "name": "United States",
          "views": 66
        },
        {
          "name": "Bangladesh",
          "views": 163
        },
        {
          "name": "India",
          "views": 140
        },
        {
          "name": "Morocco",
          "views": 32
        },
        {
          "name": "Bangladesh",
          "views": 500
        }
      ],
      "tex_content": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Manuscript prepared with the Frontiers LaTeX template, Version 3.4 (Frontiers Media SA, 2022/06/14).\n% The original template file is kept unchanged as frontiers_template_original.tex.\n% Compile with pdfLaTeX + BibTeX (Overleaf default). Figures are in figures/ and are generated by make_figures.py.\n% Note: for review readability, figures and tables are placed in the text near their first mention. Frontiers\n% re-typesets accepted articles; at submission, figures are also uploaded individually in the numbered order below.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass[utf8]{FrontiersinHarvard} % Harvard (author-date) reference style\n\\usepackage{url,hyperref,lineno,microtype,subcaption}\n\\usepackage[onehalfspacing]{setspace}\n\\usepackage{amsmath,amssymb,booktabs,multirow}\n\\usepackage{xurl}\n\\usepackage{algorithm}\n\\usepackage[noend]{algpseudocode}\n\\graphicspath{{figures/}}\n\n\\linenumbers\n\n\\def\\keyFont{\\fontsize{8}{11}\\helveticabold }\n\\def\\firstAuthorLast{Narvani {et~al.}}\n\\def\\Authors{Suresh Kumar Narvani\\,$^{1,*}$, Ipshita Kajuri\\,$^{2}$, Prakash Debnath\\,$^{3}$, Nayeem Farhan\\,$^{4}$, Najiba Hassan Apshora\\,$^{5}$, Masrufa Tasnim\\,$^{6}$, Rahul Rohit\\,$^{7}$, Sharmina Khanom\\,$^{8}$, Suchana Rani Roy\\,$^{9}$ and Wawan Devis Wahyu\\,$^{10}$}\n\\def\\Address{\n$^{1}$Department of Financial Engineering, World Quant University, Karachi, Pakistan \\\\\n$^{2}$Department of Finance, Master of Business Administration, North South University, Dhaka, Bangladesh \\\\\n$^{3}$Department of Finance, Master of Business Administration, North South University, Dhaka, Bangladesh \\\\\n$^{4}$Department of Humanities and Social Sciences, Master of Science in Finance, Newcastle University, Newcastle upon Tyne, United Kingdom \\\\\n$^{5}$Department of Pharmacy, Southeast University, Dhaka, Bangladesh \\\\\n$^{6}$Master of Business Administration (MBA)  \nHuman Resource Management\nUniversity of Dhaka\\\\\n$^{7}$Department of Finance, Independent University Bangladesh, Dhaka, Bangladesh \\\\\n$^{8}$Department of Economics and Banking, International Islamic University Chittagong, Chittagong, Bangladesh \\\\\n$^{9}$Department of Economics, Comilla Government Victoria College, Comilla, Bangladesh \\\\\n$^{10}$State Islamic Institute Kerinci, Sungai Penuh, Indonesia\n}\n\\def\\corrAuthor{Suresh Kumar Narvani}\n\\def\\corrEmail{DeaconSmawley750351@outlook.com}\n\n\\begin{document}\n\\onecolumn\n\\firstpage{1}\n\n\\title[Regime-aware conformal calibration in financial markets]{Regime-Aware Conformal Aggregation for Calibrated Return Intervals and Value-at-Risk in Financial Markets}\n\n\\author[\\firstAuthorLast ]{\\Authors}\n\\address{}\n\\correspondance{}\n\n\\extraAuth{}\n\n\\maketitle\n\n\\begin{abstract}\n\n\\section{}\nMachine-learning studies of financial markets often report high price-level accuracy from a single market, using point predictions without a random-walk comparison or any check that their uncertainty is reliable. We study the calibration of prediction intervals and value-at-risk (VaR) for daily returns under a leakage-controlled protocol, using 34 assets across equity indices, foreign exchange, commodities and cryptocurrencies (2000--2026) and a confirmation tier of 162 S\\&P~500 stocks. Eight quantile models, ranging from historical simulation and GJR-GARCH to LightGBM, an LSTM network and two ensembles, produced 90\\% intervals for one- and five-day returns. These intervals were calibrated with eleven conformal methods, including recent financial and tail-specific proposals, aggregated adaptive conformal inference (AgACI), and a new regime-aware aggregation (RA-AgCI) that learns which calibrator to trust in each real-time market regime. Evaluation used purged walk-forward cross-validation over five crisis-spanning folds, an untouched 2025--2026 hold-out, Holm-corrected Wilcoxon and paired $t$-tests, Diebold--Mariano tests, the model confidence set, VaR backtests and explainable AI. Common evaluation shortcuts mattered more than any model: smoothing the series before splitting raised the out-of-sample $R^2$ of daily return predictions from $-0.9\\%$ to $46.8\\%$, and a random walk matched every model on price-level $R^2$ (0.994). No model predicted the direction of returns, but every learned model described the return distribution better than historical simulation ($p<0.001$), with an online quantile-weighted ensemble performing best (5.7\\% lower pinball loss in cross-validation and 5.2\\% on the hold-out). For one-day intervals, RA-AgCI gave the lowest interval score on all three base models and the highest VaR-backtest pass rates (97--100\\% of assets), significantly improving on ACI and tail-specific ECI but not on global aggregation. Gains were below 1\\%, did not extend to five days, and ACI retained the smallest per-asset coverage error. On the stock tier, RA-AgCI performed best with GARCH and historical-simulation bases but not with LightGBM. Regime information is therefore most useful for models that do not adapt to volatility, and rigorous validation matters more than model choice.\n\n\\tiny\n \\keyFont{ \\section{Keywords:} uncertainty quantification, conformal prediction, value at risk, financial returns, regime shift, data leakage, model confidence set, explainable AI}\n\\end{abstract}\n\n\\section{Introduction}\n\nForecasts of financial returns and their risk underpin portfolio allocation, risk limits, margining and regulatory capital. A point forecast of tomorrow's price is of limited use for these purposes. What a risk manager needs is the distribution of possible returns, and in particular its lower tail, which is the basis of value at risk (VaR) and expected shortfall. Two stylised facts make this distribution hard to forecast: returns are close to unpredictable in mean, while their volatility is persistent and their tails are heavy \\citep{fama1970,cont2001}. Volatility models of the ARCH family were developed for exactly this structure \\citep{engle1982,bollerslev1986,glosten1993}, and the heterogeneous autoregressive (HAR) model captures the long memory of volatility with a few lagged averages \\citep{corsi2009}. Machine learning has since been applied to every part of the problem, from return prediction in the cross-section of stocks \\citep{gu2020} to deep networks for prices and risk.\n\nRecent studies in Frontiers journals illustrate both the promise and the methodological weaknesses of this literature. A review in \\emph{Frontiers in Artificial Intelligence} surveys machine learning, reinforcement learning and hybrid models for stock prediction and identifies robustness to regime shifts as ``a critical unresolved challenge across all methods''; it also warns that accurate models may have little economic value after transaction costs \\citep{rohan2026}. A deep convolutional generative adversarial network was proposed for the closing prices of Italian stocks \\citep{staffini2022}; random forests and deep networks were compared on the Karachi index before and during COVID-19 \\citep{omar2022}; a CNN-LSTM was applied to the financial indicators of Chinese listed firms \\citep{yang2025}; and an ESRNN-VAE hybrid was used to forecast the downside risk of a single South African stock \\citep{sigauke2025}. These studies share five limitations. First, accuracy is measured on price levels, where any forecaster that is close to the previous price scores well, and the random walk is not reported as a benchmark. Second, each study covers a single market or a single firm. Third, forecasts are points, or intervals whose coverage is never checked. Fourth, robustness to crises is examined by refitting the models separately in each period rather than by testing one model across a regime change. Fifth, economic value and tail-risk backtests are not reported. In some cases it is also unclear whether scaling was fitted on training data only or whether the train--test split was chronological, which leaves room for temporal leakage \\citep{bergmeir2012,cerqueira2020,albelali2025}.\n\nConformal prediction offers a model-agnostic way to obtain prediction intervals with coverage guarantees \\citep{vovk2005}. Conformalized quantile regression (CQR) adjusts the interval of any quantile model with a constant fitted on a calibration set \\citep{romano2019}. Because financial returns are dependent and non-stationary, online variants are needed: adaptive conformal inference (ACI) updates the target miscoverage level after every observation \\citep{gibbs2021}, error-quantified conformal inference (ECI) adds a feedback term proportional to the size of a miss \\citep{wu2025eci}, and bias-corrected and aggregated versions have followed \\citep{zaffran2022,lade2026}. Two 2025--2026 proposals target finance directly: temporal conformal prediction (TCP) recalibrates on a rolling window of financial returns \\citep{aich2025}, and tail-specific conformal intervals calibrate the lower and upper tails separately, so that the lower bound is itself a calibrated VaR \\citep{cuonzo2026}. It has also been argued that a training-free conformal interval should be a mandatory baseline for any learned probabilistic forecaster \\citep{manokhin2026}. What is missing is a comparison of these methods on many assets, across crises, under a protocol that excludes leakage, and with financial evaluation criteria.\n\nThis study provides such a comparison and asks four research questions.\n\\begin{itemize}\n\\item \\textbf{RQ1.} How much do common evaluation shortcuts (shuffled cross-validation, smoothing before splitting, price-level metrics) inflate the apparent accuracy of return forecasts?\n\\item \\textbf{RQ2.} How do statistical, machine-learning and deep-learning quantile forecasters compare on 34 assets in four classes, at one- and five-day horizons?\n\\item \\textbf{RQ3.} Which conformal calibration methods keep 90\\% prediction intervals calibrated across regimes and crises, and does information about the current regime help?\n\\item \\textbf{RQ4.} Do better probabilistic forecasts translate into better VaR backtests and economic value?\n\\end{itemize}\n\nThe contributions are as follows.\n\\begin{enumerate}\n\\item A leakage-controlled comparison of probabilistic return forecasters on 34 assets in four classes over 26 years, with a fresh confirmation tier of 162 stocks. All features are causal, cross-asset information is taken from strictly earlier dates, macro data are lagged for publication delay, and a future-perturbation test verifies that no feature uses future prices.\n\\item A quantification of how evaluation shortcuts inflate accuracy, showing that the effect is an order of magnitude larger than any difference between models.\n\\item A comparison of eight quantile forecasters and eleven conformal calibration methods, including TCP, tail-specific conformal prediction and bias-corrected ECI, and an online quantile-weighted ensemble based on CRPS learning \\citep{berrisch2023}.\n\\item RA-AgCI, a regime-aware aggregation of conformal calibrators. Its design was fixed on the first three folds and then confirmed on later folds, an untouched hold-out and a stock tier never used in its development.\n\\item Financial evaluation with VaR backtests \\citep{kupiec1995,christoffersen1998}, the FZ0 loss for VaR and expected shortfall \\citep{fissler2016,patton2019} and a volatility-targeting strategy \\citep{moreira2017}, together with explainable-AI analyses of what drives the tail forecasts.\n\\end{enumerate}\n\nSection~\\ref{sec:related} reviews related work. Section~\\ref{sec:methods} describes the data, features, forecasters, calibration methods and the validation and testing protocol. Section~\\ref{sec:results} reports the results for each research question, Section~\\ref{sec:discussion} discusses their implications and limitations, and Section~\\ref{sec:conclusion} concludes.\n\n\\section{Background and Related Work}\\label{sec:related}\n\n\\subsection{Predictability of returns and volatility}\n\nThe efficient-market view implies that expected returns are hard to forecast from past prices \\citep{fama1970}. Out-of-sample studies confirm that most predictors fail to beat the historical mean of equity returns \\citep{welch2008}, and even successful predictors achieve out-of-sample $R^2$ values of well under one percent at monthly frequency \\citep{campbell2008}. Machine learning can extract more signal from large cross-sections of firm characteristics \\citep{gu2020}, but daily index or currency returns offer little to work with. Volatility, in contrast, is highly predictable: squared and absolute returns are strongly autocorrelated, a pattern known as volatility clustering \\citep{cont2001}. GARCH models \\citep{engle1982,bollerslev1986} and their asymmetric GJR variant \\citep{glosten1993} describe this dynamic, HAR models approximate its long memory with daily, weekly and monthly averages \\citep{corsi2009}, and range-based estimators extract additional information from intraday highs and lows \\citep{parkinson1980,garman1980}. Because quantiles of returns depend mainly on volatility, distributional forecasting can succeed where mean forecasting fails.\n\n\\subsection{Probabilistic forecast evaluation and tail risk}\n\nProbabilistic forecasts are evaluated with proper scoring rules, which reward calibration and sharpness together \\citep{gneiting2007}. The pinball (quantile) loss evaluates individual quantiles, its average over a grid of levels approximates the continuous ranked probability score (CRPS), and the interval (Winkler) score evaluates a central prediction interval. Quantile crossing is resolved by monotone rearrangement \\citep{chernozhukov2010}. VaR forecasts are backtested with the proportion-of-failures test of \\citet{kupiec1995} and the independence and conditional-coverage tests of \\citet{christoffersen1998}. Expected shortfall is not elicitable on its own but is jointly elicitable with VaR \\citep{fissler2016}, and the FZ0 loss of \\citet{patton2019} provides a consistent joint score. Forecast accuracy is compared with Diebold--Mariano tests \\citep{diebold1995,harvey1997}, and sets of models with the model confidence set \\citep{hansen2011}.\n\n\\subsection{Conformal prediction for time series and finance}\n\nSplit conformal prediction and CQR give finite-sample coverage under exchangeability \\citep{vovk2005,romano2019}. Time series violate this assumption, and online methods address the violation. ACI adapts the nominal level by online gradient steps and guarantees long-run coverage under arbitrary distribution shift \\citep{gibbs2021}; conformal PID control adds integral and forecasting terms \\citep{angelopoulos2023}; ECI smooths the quantile loss so that the threshold reacts to the size of a miss \\citep{wu2025eci}; and bias-corrected ACI re-centres intervals after a regime change \\citep{lade2026}. Because the best ACI step size depends on the data, \\citet{zaffran2022} proposed AgACI, which runs ACI with several step sizes and aggregates their bounds with online expert weights. For finance, \\citet{aich2025} compared rolling conformal procedures on thirteen financial series and found good full-sample coverage but weaker lower-tail calibration, and \\citet{cuonzo2026} derived intervals with separate guarantees for each tail, motivated by the control of downside risk. None of these studies conditions the calibration on the market regime.\n\n\\subsection{Evaluation pitfalls}\n\nRandom K-fold cross-validation is optimistic for dependent data, and blocked or forward-chaining designs are recommended \\citep{bergmeir2012,cerqueira2020}. In finance, overlapping multi-day targets create additional leakage at fold boundaries, which is removed by purging and embargoing training observations whose label windows overlap the test period \\citep{lopezdeprado2018}. Signal-processing steps applied to the full series before splitting, such as wavelet denoising or empirical mode decomposition, leak future information into every feature \\citep{albelali2025}. Few forecasting studies document how these issues were handled.\n\n\\subsection{Research gap}\n\nThe literature reviewed above leaves a clear gap: there is no multi-asset, crisis-spanning comparison of probabilistic return forecasters and conformal calibrators under a leakage-controlled protocol, evaluated with financial criteria. Whether information about the current market regime improves calibration has not been tested.\n\n\\section{Materials and Methods}\\label{sec:methods}\n\n\\subsection{Study design}\n\nFigure~\\ref{fig:1} summarises the processing workflow. Daily prices of 34 assets and 162 stocks are cleaned and converted into causal features and volatility-standardised targets. Eight base forecasters produce eleven quantiles of the one- and five-day return. A calibration layer turns the central quantiles into 90\\% prediction intervals, and the results are evaluated against the four research questions. All code is written in Python and runs as a single Kaggle notebook. On an NVIDIA T4 GPU with four CPU cores the full run took 15.7~min; the online calibration loops were compiled with numba, and gradient-boosted models reused one binned dataset across quantile levels.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig1_workflow}\n\\end{center}\n\\caption{Processing workflow. Daily data for 34 assets, 162 stocks and two regime sources pass through four stages under a leakage-controlled protocol. \\textbf{Data preparation} (steps 1--3) acquires, cleans and explores the price, macro and geopolitical data. \\textbf{Causal features} (4--6) standardises returns by a past-only volatility estimate, builds 41 features and aligns exogenous series so that only information available at the forecast origin is used. \\textbf{Leakage-safe modelling} (7--10) assembles the pooled panel, which must pass the future-perturbation audit (a failure returns to step 7), splits it into purged walk-forward folds and a hold-out, and trains eight quantile forecasters. \\textbf{Calibrate and evaluate} (11--13) applies eleven calibration methods, including the proposed RA-AgCI, scores and tests them, and explains and confirms the results.}\\label{fig:1}\n\\end{figure}\n\n\\subsection{Data}\n\nFour public Kaggle datasets were used (Table~\\ref{tab:1}). The main dataset contains daily open, high, low and close prices and volumes for 34 assets downloaded from Yahoo Finance \\citep{belbino2026markets}: 10 equity indices (S\\&P~500, NASDAQ, DAX, FTSE~100, Nikkei~225, Hang Seng, KOSPI, Shanghai Composite, NIFTY~50 and SENSEX), 8 currency pairs against the US dollar, 8 commodity futures (WTI and Brent crude, natural gas, gold, silver, copper, corn and wheat) and 8 cryptocurrencies. It covers January 2000 to 1~October 2026; Brent and NIFTY~50 start in 2007 and most cryptocurrencies in 2017. A second dataset provides US macro-financial indicators at monthly frequency, including Treasury yield spreads, the BAA credit spread, unemployment, CPI inflation, the Sahm-rule indicator and the NBER recession flag \\citep{belbino2026macro}. A third provides the daily geopolitical risk (GPR) index of \\citet{caldara2022} up to September 2025 \\citep{dangi2025gpr}. The fourth contains daily prices of S\\&P~500 constituents from January 2010 to December 2024 \\citep{andrewmvd2024sp500}; although it lists 502 companies, prices are present for only 172, of which 162 have at least 2,500 trading days and form the stock tier.\n\n\\begin{table}[!t]\n\\centering\n\\caption{Main dataset by asset class. Annualised volatility, excess kurtosis and the left-tail Hill index \\citep{hill1975} are medians across assets; the last three columns give the share of assets for which the Jarque--Bera normality test \\citep{jarque1980}, the ADF unit-root test on log prices \\citep{dickey1979} and the Ljung--Box test on squared returns \\citep{ljung1978} reject at 5\\%.}\\label{tab:1}\n\\small\n\\begin{tabular}{lrrrrrrrr}\n\\toprule\nClass & Assets & Days & Ann. vol. & Ex. kurt. & Hill (left) & JB rej. & ADF rej. & LB($r^2$) rej. \\\\\n\\midrule\nEquity index & 10 & 64,448 & 0.23 & 8.1 & 2.98 & 100\\% & 10\\% & 100\\% \\\\\nFX & 8 & 43,751 & 0.09 & 7.4 & 3.49 & 100\\% & 38\\% & 88\\% \\\\\nCommodity & 8 & 50,557 & 0.33 & 12.8 & 2.99 & 100\\% & 25\\% & 100\\% \\\\\nCrypto & 8 & 27,250 & 1.01 & 17.2 & 2.78 & 100\\% & 0\\% & 100\\% \\\\\n\\midrule\nTotal & 34 & 186,006 & & & & & & \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Cleaning and exploratory analysis}\n\nCleaning applied five rules, each reported with a count. Rows with a non-positive close were removed; this includes WTI on 20 April 2020, when the front-month contract settled at $-37.63$ and a log return is undefined. Stale quotes, defined as an unchanged close with equal high and low, were removed; these are mostly repeated currency quotes. Inconsistent or non-positive open, high or low values were set to missing. Returns spanning gaps of more than ten calendar days were set to missing. Finally, spike-and-reverse bad prints were removed outside crypto: a one-day move of more than six past-66-day standard deviations that is at least 75\\% reversed on the next day. An example is EUR/USD, which shows $+5.9\\%$ and $-6.0\\%$ on 8 and 9 January 2008, whereas genuine jumps that do not reverse, such as the 17.6\\% rise of the Swiss franc after the Swiss National Bank removed its exchange-rate floor in January 2015, were kept. Large genuine moves in crypto and oil were kept, since tail risk is the object of study. Because this filter uses the next day's price, it is a data-quality step rather than a feature, and it is discussed as a limitation.\n\nThe exploratory analysis confirmed the usual stylised facts (Table~\\ref{tab:1}). All assets rejected normality, with median excess kurtosis from 7 (FX) to 17 (crypto), and the left-tail index was below 4 for most assets, implying an infinite fourth moment. Log prices were non-stationary for most assets, returns were stationary for all, and squared returns were autocorrelated for 33 of 34 assets, which is volatility clustering. Cross-asset correlations rose in stress periods, defined as the top decile of S\\&P~500 22-day realised volatility. The notebook reports these analyses in full, with distribution and Q--Q plots, autocorrelation functions, rolling volatility and correlation, drawdowns, calendar effects, crisis returns and the joint behaviour of GPR and equity volatility.\n\n\\subsection{Targets and causal features}\n\nLet $r_t$ be the daily log return of an asset and $\\sigma_t$ its exponentially weighted volatility ($\\lambda=0.94$), computed from returns up to and including day $t$. The target for horizon $h\\in\\{1,5\\}$ trading days is the standardised forward return\n\\begin{equation}\ny_{t,h} = \\frac{r_{t+1}+\\dots+r_{t+h}}{\\sigma_t\\sqrt{h}} .\n\\end{equation}\nStandardisation by $\\sigma_t$ removes most of the difference in scale between assets, so that one pooled (global) model can be trained across all of them and losses can be averaged and compared across assets. Forecasts of $y_{t,h}$ are converted back to returns by multiplying by $\\sigma_t\\sqrt{h}$.\n\nForty-one features were computed at each origin $t$ from data up to the close of $t$, in seven families. \\emph{Returns and momentum}: the standardised returns of the last five days, their absolute value, and momentum over 5, 22, 66 and 252 days. \\emph{Volatility}: $\\log\\sigma_t$ and the log ratios of 5-, 22-, 66- and 252-day realised volatility to $\\sigma_t$ (the HAR components), and the 22/252-day ratio that measures the volatility regime. \\emph{Range and OHLC}: Parkinson and Garman--Klass range volatility \\citep{parkinson1980,garman1980}, the intraday range, overnight gap and candle body. \\emph{Moments and technical}: 66-day skewness and kurtosis, the 252-day drawdown, distance to the 50- and 200-day moving averages, the 14-day relative strength index and a volume z-score. \\emph{Cross-asset}: the standardised return, volatility ratio and momentum of the S\\&P~500 and the cross-sectional average volatility ratio. \\emph{Macro}: the 10y--2y and 10y--3m spreads, the BAA spread, unemployment, CPI inflation and the Sahm indicator. \\emph{Calendar and class}: weekday, month and asset class.\n\nTwo alignment rules prevent look-ahead. Cross-asset features are joined with strictly earlier dates, because markets close at different times; using the US close of day $t$ for an Asian index whose day-$t$ close precedes it would leak information about the next return. Each monthly macro value is used only from the first day of the second month after its reference month, to allow for publication delay. Revisions remain a limitation because real-time vintages were not available. The NBER recession flag, which is announced with a long delay, is used only as an evaluation label. GPR is used only in an ablation, because it ends before the hold-out does.\n\n\\subsection{Leakage audit}\n\nA future-perturbation test checks that no feature depends on future prices. All prices after a cut-off date (30 June 2015) were multiplied by random noise for four assets, including the S\\&P~500 that feeds the cross-asset features, and the panel was rebuilt. Every feature on or before the cut-off was bit-identical to the original (maximum absolute difference 0, no change in missing-value patterns), while targets that extend past the cut-off changed as expected. The notebook stops if this test fails.\n\n\\subsection{Validation design}\n\nThe forecasts were evaluated with an expanding-window, purged, walk-forward cross-validation with five folds, followed by an untouched hold-out (Figure~\\ref{fig:2}). The test blocks were 2006--2009 (including the global financial crisis), 2010--2013 (euro debt crisis), 2014--2017 (China and oil sell-off), 2018--2021 (COVID-19) and 2022--2024 (rate shock and crypto collapse); the hold-out covers 1 January 2025 to 1 October 2026, including the April 2025 tariff shock. In each fold, the two years before the test block form the calibration block, and all earlier observations form the fit block. Any observation whose target window extends into a later block is purged from the earlier one, so that no training or calibration label overlaps a test label. An asset enters a fold only with at least 500 fit and 120 calibration observations, so that most cryptocurrencies enter from fold 4 or 5. The folds contain 17, 23, 26, 26 and 33 assets and 117,650 test observations at $h=1$; the hold-out contains 34 assets and 15,983 observations. The stock tier uses the same design with five two-year folds from 2015 to 2024 and 397,885 test observations. No hyper-parameter or method choice used test data: model hyper-parameters were tuned on an inner split of the fit block, and calibration step sizes were selected on the last 40\\% of the calibration block.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig2_validation}\n\\end{center}\n\\caption{Validation design. Expanding fit blocks (blue) are followed by a two-year calibration block (amber) and a test block; observations whose targets overlap the next block are purged. The five CV test blocks (orange) each contain a crisis (red bands); the 2025--2026 hold-out (black) was not used for any design decision.}\\label{fig:2}\n\\end{figure}\n\n\\subsection{Base forecasters}\n\nEach forecaster outputs eleven quantiles of $y_{t,h}$ at levels $\\tau$ = 0.01, 0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.975 and 0.99, sorted to remove crossing \\citep{chernozhukov2010}.\n\\begin{itemize}\n\\item \\textbf{CN-Floor} is the training-free conformal floor of \\citet{manokhin2026}: a zero-return point forecast with symmetric quantiles from the split-conformal distribution of absolute $h$-day returns, fitted per asset. It does not adapt to volatility.\n\\item \\textbf{HS-500} is historical simulation: rolling empirical quantiles of the last 500 $h$-day returns.\n\\item \\textbf{GJR-GARCH-t} is a GJR-GARCH(1,1) model with Student-$t$ innovations \\citep{glosten1993}, estimated per asset on the fit block and filtered through the calibration and test blocks with frozen parameters. Five-day quantiles use the summed analytic variance with the fitted $t$ shape, an approximation.\n\\item \\textbf{HAR-QR} is a linear quantile regression of the target on the HAR volatility components and the last absolute return, pooled across assets \\citep{corsi2009}.\n\\item \\textbf{LightGBM-QR} is a pooled gradient-boosted tree model \\citep{ke2017} with one model per quantile level and all 41 features. The number of leaves, the minimum leaf size and the number of boosting rounds were chosen on an inner validation set: the last year of the fit block, purged from the training part. The tuning considered four configurations and early stopping on the pinball loss at $\\tau\\in\\{0.05,0.5,0.95\\}$.\n\\item \\textbf{LSTM-QR} is a pooled long short-term memory network \\citep{hochreiter1997} with one 64-unit layer over a 60-day window of nine input channels, plus a one-hot asset class, trained for ten epochs with the joint pinball loss of both horizons. Input scaling was fitted on the fit block, and the output layer was initialised at standard normal quantiles.\n\\item \\textbf{Ensemble} averages the quantiles of GARCH, HAR-QR, LightGBM and LSTM with equal weights.\n\\item \\textbf{QW-Ensemble} combines the same four models with online quantile-specific weights, a form of CRPS learning \\citep{berrisch2023}. For each quantile level, exponentially weighted averaging updates the weights with the pinball loss of each model as soon as the label is observed; the learning rate is selected on the calibration block.\n\\end{itemize}\n\n\\subsection{Conformal calibration}\n\nAll calibration methods act on the central 90\\% interval $[\\hat q_{0.05}, \\hat q_{0.95}]$ ($\\alpha=0.1$) of three base forecasters (GJR-GARCH-t, LightGBM-QR and QW-Ensemble), with the CQR score $s=\\max(\\hat q_{0.05}-y,\\;y-\\hat q_{0.95})$ or, for tail-specific methods, the one-sided scores $s^{\\mathrm{lo}}=\\hat q_{0.05}-y$ and $s^{\\mathrm{up}}=y-\\hat q_{0.95}$ at level $\\alpha/2$ each. Labels are used with delayed feedback: an $h$-day label becomes available only at origins on or after the end of its target window. Table~\\ref{tab:2} lists the eleven methods. The static methods use the full calibration block. The online methods initialise their thresholds on the first 60\\% of the calibration block, choose their step sizes by the Winkler score on the remaining 40\\%, and then run through the test block.\n\n\\begin{table}[!t]\n\\centering\n\\caption{Calibration methods. ``Tail'' indicates separate lower and upper thresholds; ``Keyed by'' is the unit for which thresholds or weights are maintained.}\\label{tab:2}\n\\small\n\\begin{tabular}{p{2.6cm}p{6.3cm}p{1.1cm}p{1.9cm}p{2.1cm}}\n\\toprule\nMethod & Mechanism & Tail & Keyed by & Reference \\\\\n\\midrule\nRaw & Model quantiles $[\\hat q_{0.05},\\hat q_{0.95}]$ & -- & -- & -- \\\\\nSplit CQR & Static conformal constant & no & asset & \\citet{romano2019} \\\\\nTail-split CP & Static constants per tail & yes & asset & \\citet{cuonzo2026} \\\\\nTCP & Rolling 250-score conformal quantile & no & asset & \\citet{aich2025} \\\\\nACI & Online update of the miscoverage level & no & asset & \\citet{gibbs2021} \\\\\nECI & Online threshold with error-quantified feedback & no & asset & \\citet{wu2025eci} \\\\\nBC-ECI & ECI on bias-corrected scores & no & asset & \\citet{lade2026} \\\\\nTS-ECI & ECI per tail & yes & asset & this study \\\\\nRCT-ECI & ECI per tail, pooled within regime groups & yes & regime & this study \\\\\nAgACI & EWA aggregation of 9 calibrators & yes & global & \\citet{zaffran2022} \\\\\n\\textbf{RA-AgCI} & EWA aggregation of 9 calibrators, one weight vector per regime & yes & regime & this study \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsubsection{Regime-aware aggregated conformal inference (RA-AgCI)}\n\nThe idea behind RA-AgCI is that different calibrators are best in different market conditions. A slowly adapting ACI is efficient in calm markets, a fast tail-specific ECI is preferable when volatility jumps, and a regime-pooled threshold may help in rare states where an asset's own history is short. RA-AgCI runs a pool of $K=9$ calibrators and combines their bounds with online exponentially weighted averaging (EWA), separately for the lower and the upper bound and separately for each real-time regime group. The pool consists of ACI, tail-specific ACI with step sizes $\\gamma\\in\\{0.001,0.005,0.02,0.05\\}$, TS-ECI, TS-ECI with steps doubled in stress and high-volatility states, RCT-ECI, and TS-ECI on scores normalised by a regime-dependent scale.\n\nThe regime group $g_t$ of an observation is defined from information available at origin $t$: the asset class, the tercile of the 22/252-day volatility ratio (with tercile boundaries from the fit block), and a market-stress flag indicating that the S\\&P~500 22-day realised volatility, observed on the previous day, exceeds the 80th percentile of the fit block. This gives up to 24 groups, pooled across assets in standardised units. The lower bound is $L_t=\\sum_k w^{\\mathrm{lo}}_{g_t,k}L^{(k)}_t$ and the upper bound $U_t=\\sum_k w^{\\mathrm{up}}_{g_t,k}U^{(k)}_t$. When the label $y_r$ of an earlier origin $r$ becomes available, the weights of group $g_r$ are updated with the pinball loss at the matching tail level:\n\\begin{equation}\nw^{\\mathrm{lo}}_{g,k}\\propto w^{\\mathrm{lo}}_{g,k}\\exp\\{-\\eta\\,\\rho_{\\alpha/2}(y_r-L^{(k)}_r)\\},\\qquad\nw^{\\mathrm{up}}_{g,k}\\propto w^{\\mathrm{up}}_{g,k}\\exp\\{-\\eta\\,\\rho_{1-\\alpha/2}(y_r-U^{(k)}_r)\\},\n\\end{equation}\nwhere $\\rho_\\tau(u)=\\max\\{\\tau u,(\\tau-1)u\\}$, followed by optional fixed-share mixing $w\\leftarrow(1-\\beta)w+\\beta/K$ to track changes. The learning rate $\\eta\\in\\{0.5,2,8\\}$ and $\\beta\\in\\{0,0.02\\}$ are chosen on the calibration block. Because the pinball loss at level $\\alpha/2$ is the proper score for the $\\alpha/2$ quantile, each bound is pulled towards a calibrated tail quantile, and the lower bound is directly a 5\\% VaR forecast. AgACI is the special case with a single global group. Figure~\\ref{fig:3} illustrates the mechanism and Algorithm~\\ref{alg:1} summarises the procedure.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig3_raagci}\n\\end{center}\n\\caption{Regime-aware aggregated conformal inference (RA-AgCI). The raw 90\\% interval of a base model is recalibrated by a pool of nine conformal experts, each giving lower and upper bounds. The regime of the origin $t$ (asset class $\\times$ volatility tercile $\\times$ market-stress flag, from information up to $t$) selects one row of a weight table with up to 24 groups; each row holds separate expert weights for the lower and the upper bound (bar segments). The aggregated bounds form the calibrated interval, whose lower end is the 5\\% VaR. When an outcome $y_r$ is observed $h$ days later, the pinball loss of each expert at the matching tail level updates the weights of the group $g_r$ in which that prediction was made (delayed feedback).}\\label{fig:3}\n\\end{figure}\n\n\\begin{algorithm}[!t]\n\\caption{RA-AgCI for one base forecaster and horizon}\\label{alg:1}\n\\begin{algorithmic}[1]\n\\Require stream of origins sorted by date; expert bounds $(L^{(k)}_t,U^{(k)}_t)_{k=1}^K$; regime group $g_t$; target end date $e_t$; $\\eta$, $\\beta$\n\\State initialise $w^{\\mathrm{lo}}_{g}=w^{\\mathrm{up}}_{g}=(1/K,\\dots,1/K)$ for every group\n\\For{each origin $t$ in date order}\n  \\For{each earlier origin $r$ with $e_r\\le t$ not yet used} \\Comment{delayed feedback}\n    \\State update $w^{\\mathrm{lo}}_{g_r}$ and $w^{\\mathrm{up}}_{g_r}$ by EWA on $\\rho_{\\alpha/2}(y_r-L^{(k)}_r)$ and $\\rho_{1-\\alpha/2}(y_r-U^{(k)}_r)$; mix with $\\beta/K$\n  \\EndFor\n  \\State $L_t\\gets\\sum_k w^{\\mathrm{lo}}_{g_t,k}L^{(k)}_t$, \\quad $U_t\\gets\\sum_k w^{\\mathrm{up}}_{g_t,k}U^{(k)}_t$ \\Comment{$L_t$ is the 5\\% VaR}\n\\EndFor\n\\end{algorithmic}\n\\end{algorithm}\n\n\\emph{Design protocol.} RA-AgCI was not the first proposal. An earlier version, RCT-ECI, pooled ECI thresholds within regime groups; in a first full run it did not beat ACI. Fourteen single-calibrator variants and five aggregation groupings (global, per asset, per class, 6 and 24 regime groups) were then compared using folds 1--3 only, and the variant with the best mean rank on the Winkler score and per-asset coverage error across both horizons and two base models was frozen. It was then confirmed on folds 4--5 and the hold-out, which had been seen in the first run for other methods, and on the stock tier, which was never used in its design. We report this history so that the results can be judged accordingly.\n\n\\subsection{Evaluation metrics}\n\nAll metrics were computed in standardised units, which makes them comparable across assets. Point accuracy of the median was measured by the out-of-sample $R^2$ against the zero-return random walk, $R^2_{\\mathrm{oos}}=1-\\sum(y-\\hat q_{0.5})^2/\\sum y^2$ \\citep{campbell2008}, and by directional accuracy. To reproduce the metrics of the reviewed studies, median forecasts were also converted to price forecasts and scored by price-level $R^2$ and MAPE. Distributional accuracy was measured by the pinball loss averaged over the eleven levels and by the CRPS approximated on the quantile grid \\citep{gneiting2007}, with skill expressed as the percentage reduction relative to HS-500. Intervals were evaluated by the prediction-interval coverage probability (PICP), the mean per-asset absolute coverage error $|\\mathrm{PICP}-0.9|$, the lower- and upper-tail miss rates, the mean width and the Winkler score. The 5\\% and 1\\% VaR were backtested per asset with the Kupiec and Christoffersen tests \\citep{kupiec1995,christoffersen1998}, reporting the share of assets that pass at the 5\\% level. The joint VaR and expected-shortfall forecast was scored with the FZ0 loss \\citep{patton2019}, with the 5\\% expected shortfall approximated from the 1\\%, 2.5\\% and 5\\% quantiles. Economic value was measured with a volatility-targeting strategy \\citep{moreira2017}: the position is $w_t=\\min\\{2,(0.10/\\sqrt{252})/\\hat\\sigma_t\\}$, where $\\hat\\sigma_t$ is the interval width divided by 3.29 and rescaled to returns, with transaction costs of 2 (FX), 5 (indices), 10 (commodities) and 20 (crypto) basis points per unit of turnover. We report the distance of the realised volatility from the 10\\% target, the Sharpe ratio and the maximum drawdown.\n\n\\subsection{Statistical testing}\n\nThe main unit of comparison is the asset: each model's loss was averaged over all CV test observations of an asset, and models were compared with the paired $t$-test and the Wilcoxon signed-rank test \\citep{wilcoxon1945}, with Holm correction within each family \\citep{holm1979}. Effect sizes are Cohen's $d_z$ and the rank-biserial correlation. For each asset, Diebold--Mariano tests with heteroskedasticity- and autocorrelation-consistent variance and the small-sample correction of \\citet{harvey1997} compared daily loss differences \\citep{diebold1995}. The model confidence set \\citep{hansen2011} was computed on the cross-asset daily mean pinball loss with a block bootstrap, and the notebook additionally reports Friedman ranks with the Nemenyi critical difference \\citep{friedman1937,demsar2006}. Confidence intervals for coverage used a moving-block bootstrap \\citep{kunsch1989}.\n\n\\subsection{Explainability}\n\nTreeSHAP values \\citep{lundberg2020} of the LightGBM 5\\%, 50\\% and 95\\% quantile models were computed on 5,000 test observations of fold 5, and summarised by feature family, by market state and across folds. Permutation importance by feature family measured the increase in the 5\\% pinball loss when all features of a family were permuted together. For the LSTM, gradient-times-input saliency over channels and lags was computed in the notebook.\n\n\\section{Results}\\label{sec:results}\n\n\\subsection{RQ1: evaluation shortcuts and the price-level illusion}\n\nThe protocol mattered far more than the model (Figure~\\ref{fig:4}). Under the purged walk-forward protocol, the LightGBM median forecast had an out-of-sample $R^2$ of $-0.9\\%$ at $h=1$ and $-5.3\\%$ at $h=5$, and a directional accuracy of 50\\%: as expected for liquid markets, there was no predictable mean. Shuffled five-fold cross-validation raised the five-day $R^2$ to $+10.8\\%$ and the directional accuracy to 64\\%, because overlapping five-day targets of neighbouring days fall into both training and test folds. Adding two centred moving averages, computed on the full series before splitting, raised the one-day $R^2$ to $+46.8\\%$ and the directional accuracy to 72\\%. Price-level metrics were uninformative in a different way: the random walk achieved a price $R^2$ of 0.994 and a MAPE of 1.09\\% at $h=1$, the same as every learned model, even though none of them beat the random walk on returns.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig4_leakage}\n\\end{center}\n\\caption{Evaluation shortcuts. \\textbf{(A)} Out-of-sample $R^2$ and \\textbf{(B)} directional accuracy of the LightGBM median under (A) purged walk-forward validation, (B) shuffled five-fold cross-validation, (C) walk-forward validation with centred smoothing computed on the full series, and (D) both. \\textbf{(C)} Price-level $R^2$ and MAPE are identical for the random walk and the learned models, although no model beats the random walk on returns.}\\label{fig:4}\n\\end{figure}\n\n\\subsection{RQ2: base forecaster skill}\n\nEvery learned model improved on historical simulation in distribution (Table~\\ref{tab:3}, Figure~\\ref{fig:5}). At $h=1$ in cross-validation, the pinball loss fell by 3.5\\% for GJR-GARCH-t, 3.6\\% for HAR-QR, 4.3\\% for the LSTM, 4.9\\% for the equal-weight ensemble, 5.6\\% for the tuned LightGBM and 5.7\\% for the QW-Ensemble. All improvements were significant across assets with large effect sizes (Holm-adjusted Wilcoxon and $t$-test $p<0.001$; Cohen's $d_z$ from $-1.5$ to $-2.4$). The ranking was stable across folds (Figure~\\ref{fig:5}A) and held on the hold-out, where the QW-Ensemble again ranked first (5.2\\%), followed by LightGBM (5.1\\%). The QW-Ensemble was the only model in the 90\\% model confidence set, and it beat HS-500 in Diebold--Mariano tests on all assets, compared with 97\\% for LightGBM, 94\\% for the ensemble and the LSTM, 91\\% for HAR-QR and 88\\% for GARCH. Its learned weights concentrated on LightGBM, so its advantage over LightGBM alone was small, although significant ($p<0.001$). The training-free CN-Floor was 4.1\\% worse than historical simulation because it ignores the volatility state.\n\n\\begin{table}[!t]\n\\centering\n\\caption{Base forecasters. Pinball loss is in standardised units; skill is the reduction relative to HS-500. Coverage is that of the raw 90\\% interval. All learned models beat HS-500 at both horizons (Holm-adjusted Wilcoxon $p<0.001$). $^\\dagger$Only model in the 90\\% model confidence set (CV, $h=1$).}\\label{tab:3}\n\\small\n\\begin{tabular}{lrrrrrrrr}\n\\toprule\n& \\multicolumn{4}{c}{CV (2006--2024)} & \\multicolumn{4}{c}{Hold-out (2025--2026)} \\\\\n\\cmidrule(lr){2-5}\\cmidrule(lr){6-9}\n& \\multicolumn{2}{c}{$h=1$} & \\multicolumn{2}{c}{$h=5$} & \\multicolumn{2}{c}{$h=1$} & \\multicolumn{2}{c}{$h=5$} \\\\\nModel & Pinball & Skill & Skill & PICP$_{h=1}$ & Pinball & Skill & Skill & PICP$_{h=1}$ \\\\\n\\midrule\nCN-Floor & 0.1824 & $-4.1\\%$ & $-3.3\\%$ & 0.913 & 0.1815 & $-4.6\\%$ & $-3.8\\%$ & 0.914 \\\\\nHS-500 & 0.1751 & 0 & 0 & 0.892 & 0.1735 & 0 & 0 & 0.880 \\\\\nGJR-GARCH-t & 0.1690 & 3.5\\% & 2.8\\% & 0.902 & 0.1700 & 2.0\\% & 1.1\\% & 0.913 \\\\\nHAR-QR & 0.1688 & 3.6\\% & 3.0\\% & 0.899 & 0.1698 & 2.1\\% & 0.7\\% & 0.905 \\\\\nLSTM-QR & 0.1676 & 4.3\\% & 3.3\\% & 0.893 & 0.1657 & 4.5\\% & 2.5\\% & 0.899 \\\\\nLightGBM-QR & 0.1653 & 5.6\\% & 2.6\\% & 0.899 & 0.1646 & 5.1\\% & 2.0\\% & 0.906 \\\\\nEnsemble & 0.1665 & 4.9\\% & \\textbf{3.8\\%} & 0.903 & 0.1661 & 4.2\\% & \\textbf{2.6\\%} & 0.913 \\\\\nQW-Ensemble$^\\dagger$ & \\textbf{0.1652} & \\textbf{5.7\\%} & 3.4\\% & 0.899 & \\textbf{0.1645} & \\textbf{5.2\\%} & 2.0\\% & 0.905 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nAt five days the gains were smaller and the ranking changed. The equal-weight ensemble was best (3.8\\% in CV, 2.6\\% on the hold-out), and LightGBM fell to 2.6\\% with an under-covering raw interval (PICP 0.888). Inner-validation tuning mattered here: in a first run with fixed hyper-parameters, LightGBM had been worse than historical simulation at $h=5$ ($-0.3\\%$) with a coverage of 0.847, and the tuned model usually chose larger minimum leaf sizes and fewer rounds. The raw intervals of the learned models were already close to nominal coverage at $h=1$ (0.893--0.903), which leaves little room for calibration.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig5_models}\n\\end{center}\n\\caption{Base forecaster skill. \\textbf{(A)} Pinball-loss skill relative to HS-500 by CV fold and on the hold-out (HO), $h=1$. \\textbf{(B)} Skill in cross-validation and on the hold-out at both horizons.}\\label{fig:5}\n\\end{figure}\n\n\\subsection{RQ3: calibration across regimes}\n\nCalibration effects were small but systematic (Table~\\ref{tab:4}, Figure~\\ref{fig:6}). At $h=1$ in cross-validation, RA-AgCI gave the lowest Winkler score for all three base models: 4.4646 for LightGBM, 4.4635 for the QW-Ensemble and 4.6359 for GARCH, against 4.4714, 4.4714 and 4.6768 for the raw intervals. Its coverage was 0.900--0.902, and its lower-tail miss rate was 0.050 for every base. The improvement over ACI was significant for GARCH (Holm-adjusted Wilcoxon $p=0.017$) and the QW-Ensemble ($p=0.004$), and over TS-ECI for LightGBM ($p=0.018$) and the QW-Ensemble ($p=0.002$), but RA-AgCI was not significantly different from AgACI with any base (Table~\\ref{tab:5}). ACI kept the smallest per-asset coverage error with every base (0.0019--0.0029, against 0.0033--0.0052 for RA-AgCI; $p\\le0.005$). In the VaR backtests, the RA-AgCI lower bound passed the Kupiec test for 97\\% (GARCH) to 100\\% (LightGBM, QW-Ensemble) of assets and the Christoffersen conditional-coverage test for 94--97\\%, the highest or joint-highest pass rates of all methods. Raw intervals passed for 45--58\\% and ACI for 52--94\\%.\n\n\\begin{table}[!t]\n\\centering\n\\caption{Calibration of the 90\\% interval of the QW-Ensemble at $h=1$. $|$ACE$|$ is the mean per-asset absolute coverage error; Kupiec and CC are the shares of assets passing the 5\\% VaR backtests of the lower bound. Best values in bold.}\\label{tab:4}\n\\small\n\\begin{tabular}{lrrrrrrrrr}\n\\toprule\n& \\multicolumn{5}{c}{CV (2006--2024)} & \\multicolumn{4}{c}{Hold-out (2025--2026)} \\\\\n\\cmidrule(lr){2-6}\\cmidrule(lr){7-10}\nMethod & PICP & $|$ACE$|$ & Winkler & Kupiec & CC & PICP & Winkler & Kupiec & CC \\\\\n\\midrule\nRaw & 0.899 & 0.0106 & 4.4714 & 58\\% & 52\\% & 0.905 & 4.5318 & 88\\% & 88\\% \\\\\nSplit CQR & 0.895 & 0.0109 & 4.4749 & 58\\% & 61\\% & 0.905 & \\textbf{4.5300} & 82\\% & 94\\% \\\\\nTail-split CP & 0.897 & 0.0101 & 4.4761 & 55\\% & 67\\% & 0.905 & 4.5364 & 85\\% & 88\\% \\\\\nTCP & 0.911 & 0.0109 & 4.4777 & 64\\% & 70\\% & 0.912 & 4.5433 & 82\\% & 79\\% \\\\\nACI & 0.900 & \\textbf{0.0019} & 4.4748 & 94\\% & 85\\% & 0.904 & 4.5418 & 94\\% & \\textbf{97\\%} \\\\\nECI & 0.897 & 0.0046 & 4.4755 & 82\\% & 85\\% & 0.903 & 4.5436 & 94\\% & \\textbf{97\\%} \\\\\nBC-ECI & 0.897 & 0.0046 & 4.4845 & 88\\% & 85\\% & 0.902 & 4.5677 & 97\\% & 94\\% \\\\\nTS-ECI & 0.898 & 0.0038 & 4.4678 & 97\\% & \\textbf{97\\%} & 0.904 & 4.5412 & \\textbf{100\\%} & \\textbf{97\\%} \\\\\nRCT-ECI & 0.898 & 0.0089 & 4.4795 & 73\\% & 73\\% & 0.902 & 4.5363 & 88\\% & 91\\% \\\\\nAgACI & 0.899 & 0.0037 & 4.4653 & \\textbf{100\\%} & 94\\% & 0.905 & 4.5368 & 94\\% & \\textbf{97\\%} \\\\\nRA-AgCI & 0.900 & 0.0039 & \\textbf{4.4635} & \\textbf{100\\%} & \\textbf{97\\%} & 0.904 & 4.5378 & \\textbf{100\\%} & \\textbf{97\\%} \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig6_calibration}\n\\end{center}\n\\caption{Calibration at $h=1$. \\textbf{(A)} Coverage against the change in Winkler score relative to the raw interval, for three base models (marker shape) and eleven methods (colour) in cross-validation; RA-AgCI is outlined. \\textbf{(B)} Share of assets passing the Kupiec and Christoffersen 5\\% VaR backtests for the QW-Ensemble base.}\\label{fig:6}\n\\end{figure}\n\n\\begin{table}[!t]\n\\centering\n\\caption{RA-AgCI against the strongest comparators in cross-validation: mean per-asset Winkler score and $|$ACE$|$ (RA-AgCI vs comparator) with Holm-adjusted Wilcoxon $p$-values over 33 assets. Bold: RA-AgCI significantly better; italic: significantly worse.}\\label{tab:5}\n\\footnotesize\\setlength{\\tabcolsep}{3.5pt}\n\\begin{tabular}{llrrrrrr}\n\\toprule\n& & \\multicolumn{2}{c}{vs ACI} & \\multicolumn{2}{c}{vs TS-ECI} & \\multicolumn{2}{c}{vs AgACI} \\\\\n\\cmidrule(lr){3-4}\\cmidrule(lr){5-6}\\cmidrule(lr){7-8}\n$h$ & Base & Winkler & $|$ACE$|$ & Winkler & $|$ACE$|$ & Winkler & $|$ACE$|$ \\\\\n\\midrule\n1 & GJR-GARCH-t & \\textbf{4.703 vs 4.716} & \\emph{0.005 vs 0.003} & 4.703 vs 4.708 & 0.005 vs 0.005 & 4.703 vs 4.708 & 0.005 vs 0.006 \\\\\n  & & \\textbf{$p$=0.017} & \\emph{$p$=0.001} & $p$=0.25 & $p$=1.0 & $p$=0.25 & $p$=1.0 \\\\\n1 & LightGBM-QR & 4.530 vs 4.535 & \\emph{0.003 vs 0.002} & \\textbf{4.530 vs 4.535} & 0.003 vs 0.004 & 4.530 vs 4.529 & 0.003 vs 0.004 \\\\\n  & & $p$=0.11 & \\emph{$p$=0.005} & \\textbf{$p$=0.018} & $p$=0.21 & $p$=0.96 & $p$=0.32 \\\\\n1 & QW-Ensemble & \\textbf{4.527 vs 4.538} & \\emph{0.004 vs 0.002} & \\textbf{4.527 vs 4.533} & 0.004 vs 0.004 & 4.527 vs 4.529 & 0.004 vs 0.004 \\\\\n  & & \\textbf{$p$=0.004} & \\emph{$p$<0.001} & \\textbf{$p$=0.002} & $p$=1.0 & $p$=0.35 & $p$=1.0 \\\\\n\\midrule\n5 & GJR-GARCH-t & 4.838 vs 4.826 & \\emph{0.006 vs 0.003} & 4.838 vs 4.824 & 0.006 vs 0.006 & 4.838 vs 4.838 & 0.006 vs 0.006 \\\\\n  & & $p$=1.0 & \\emph{$p$=0.008} & $p$=0.64 & $p$=0.95 & $p$=1.0 & $p$=0.22 \\\\\n5 & LightGBM-QR & \\emph{4.841 vs 4.811} & \\emph{0.008 vs 0.004} & \\emph{4.841 vs 4.820} & \\emph{0.008 vs 0.006} & 4.841 vs 4.842 & 0.008 vs 0.008 \\\\\n  & & \\emph{$p$=0.015} & \\emph{$p$<0.001} & \\emph{$p$=0.018} & \\emph{$p$=0.002} & $p$=0.87 & $p$=1.0 \\\\\n5 & QW-Ensemble & \\emph{4.848 vs 4.811} & \\emph{0.008 vs 0.004} & \\emph{4.848 vs 4.821} & \\emph{0.008 vs 0.004} & \\emph{4.848 vs 4.811} & 0.008 vs 0.006 \\\\\n  & & \\emph{$p$=0.002} & \\emph{$p$<0.001} & \\emph{$p$=0.005} & \\emph{$p$<0.001} & \\emph{$p$=0.002} & $p$=0.29 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\nAt $h=5$ the picture reversed. RA-AgCI was significantly worse than ACI and TS-ECI for LightGBM and the QW-Ensemble, and worse than AgACI for the QW-Ensemble (Table~\\ref{tab:5}). With overlapping five-day labels, the feedback that drives the weights arrives five days late and is strongly autocorrelated, and regime-specific weights, which split this feedback into up to 24 groups, adapted too slowly. On the hold-out at $h=1$ all calibrated methods were within 0.9\\% of each other in Winkler score, and the raw QW-Ensemble interval was already close to nominal (PICP 0.905).\n\nCalibration mattered most in crises (Figure~\\ref{fig:7}). During the global financial crisis, raw QW-Ensemble intervals covered 87.4\\% of outcomes and missed the lower tail 7.6\\% of the time; RA-AgCI restored coverage to 90.0\\% and reduced the lower-tail misses to 5.5\\%. In the euro debt crisis, coverage rose from 87.2\\% to 89.4\\% and lower-tail misses fell from 8.2\\% to 5.7\\%, the best of the methods in Figure~\\ref{fig:7}, and in NBER recessions from 88.0\\% to 90.0\\%. COVID-19 remained the hardest episode: all methods under-covered (84--87\\%), with RA-AgCI the least affected (86.5\\% coverage, 8.3\\% lower-tail misses against 9.5\\% raw and 10.2\\% for split CQR). The April 2025 tariff shock, in the hold-out, behaved similarly (85.8\\% raw, 86.7\\% for RA-AgCI and TS-ECI). Static split CQR did not help in crises, and in COVID-19 it made coverage worse, because its constant was fitted in the calmer calibration years. In the 2022 rate shock and the crypto collapse, raw intervals over-covered (92\\%), and all online methods narrowed them towards 90\\%.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig7_regimes}\n\\end{center}\n\\caption{Calibration by regime, QW-Ensemble base, $h=1$, CV and hold-out pooled. \\textbf{(A)} 90\\% coverage and \\textbf{(B)} lower-tail miss rate (target 0.05) for calm periods, market stress (top-decile S\\&P~500 volatility), NBER recessions, high geopolitical risk and seven named crises.}\\label{fig:7}\n\\end{figure}\n\n\\subsubsection{Confirmation on 162 stocks}\n\nThe stock tier tested RA-AgCI on data never used in its design (Figure~\\ref{fig:8}). The base models ranked as in the main tier: LightGBM 3.3\\% and GJR-GARCH-t 2.5\\% better than historical simulation, CN-Floor 0.5\\% worse (all $p<0.001$). With the GARCH base, RA-AgCI had the lowest Winkler score of all eleven methods (4.852), significantly better than every other method including AgACI (Holm $p\\le0.0003$). With the historical-simulation base, RA-AgCI improved the Winkler score by 2.2\\% over ACI, 3.4\\% over TS-ECI and 5.8\\% over split CQR (all $p<0.001$), and it was tied with RCT-ECI ($p=0.33$), the other regime-aware method. With the LightGBM base, however, RA-AgCI was 0.1--0.3\\% worse than the raw interval, split CQR, ACI, TS-ECI and RCT-ECI ($p\\le0.011$), while it had the highest Kupiec pass rate (97.6\\% of stock-folds). As in the main tier, ACI had the smallest coverage error with every base.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig8_stocks}\n\\end{center}\n\\caption{Confirmation tier, 162 S\\&P~500 stocks, $h=1$, 2015--2024. \\textbf{(A)} Winkler score of RA-AgCI relative to each other method for three base models; negative values favour RA-AgCI; * marks Holm-adjusted Wilcoxon $p<0.05$. \\textbf{(B)} Share of stock-folds passing the Kupiec 5\\% VaR test.}\\label{fig:8}\n\\end{figure}\n\n\\subsection{RQ4: tail risk and economic value}\n\nBetter distributional forecasts improved tail-risk scores. The FZ0 loss for the joint 5\\% VaR and expected-shortfall forecast was 0.827 for the QW-Ensemble and LightGBM, 0.851 for the ensemble, 0.898 for GARCH, 1.018 for HS-500 and 1.105 for CN-Floor in cross-validation (0.777 against 0.984 for HS-500 on the hold-out). Raw 1\\% VaR forecasts were harder to calibrate: the share of assets passing the Kupiec test at 1\\% ranged from 24\\% (CN-Floor) to 61\\% (ensemble), with hit rates of 1.2--1.4\\% for the learned models, which reflects the heavy left tails documented in Table~\\ref{tab:1}.\n\nEconomic value appeared in risk control rather than in returns (Table~\\ref{tab:6}). A strategy that targets 10\\% annual volatility using the forecast interval width achieved a realised volatility within 0.5--0.6 percentage points of the target with the ensembles and LightGBM, against 1.1 with historical simulation and 1.6 with the conformal floor; on the hold-out the gap widened (0.6 against 2.0 and 3.0). Sharpe ratios after costs were not improved: the smoother position changes of historical simulation produced the highest Sharpe ratio (0.10 in CV, 0.38 on the hold-out), while the more responsive learned forecasts traded more and earned 0.06 in CV. Strategies that bet on the sign of the median forecast gave inconsistent results. In cross-validation the equal-weight ensemble reached a Sharpe ratio of 0.14 against 0.09 for buy-and-hold, but HAR-QR and HS-500 were negative ($-0.09$ and $-0.07$) and LightGBM was close to zero (0.02); on the hold-out, the ensemble, LSTM and QW-Ensemble exceeded buy-and-hold (0.55, 0.49 and 0.46 against 0.35) while LightGBM did not ($-0.02$). Given the directional accuracy of 50\\% and the non-positive out-of-sample $R^2$ (RQ1), and since Sharpe-ratio differences were not tested for significance, we do not interpret these results as evidence of directional predictability.\n\n\\begin{table}[!t]\n\\centering\n\\caption{Tail risk and economic value at $h=1$. FZ0 is the joint VaR and expected-shortfall loss (lower is better); Kupiec 1\\% is the share of assets passing at the 1\\% VaR level; tracking error is the absolute distance (percentage points) of the realised annual volatility from the 10\\% target of the volatility-targeting strategy; Sharpe ratios are after transaction costs. Buy-and-hold has a Sharpe ratio of 0.09 (CV) and 0.35 (hold-out).}\\label{tab:6}\n\\small\n\\begin{tabular}{lrrrrrrr}\n\\toprule\n& \\multicolumn{4}{c}{CV (2006--2024)} & \\multicolumn{3}{c}{Hold-out (2025--2026)} \\\\\n\\cmidrule(lr){2-5}\\cmidrule(lr){6-8}\nModel & FZ0 & Kupiec 1\\% & Track. err. & Sharpe & FZ0 & Track. err. & Sharpe \\\\\n\\midrule\nCN-Floor & 1.105 & 24\\% & 1.58 & 0.09 & 1.095 & 3.01 & 0.35 \\\\\nHS-500 & 1.018 & 48\\% & 1.10 & \\textbf{0.10} & 0.984 & 1.99 & \\textbf{0.38} \\\\\nGJR-GARCH-t & 0.898 & 48\\% & 0.72 & 0.07 & 0.873 & 0.98 & 0.32 \\\\\nHAR-QR & 0.893 & 58\\% & 0.55 & 0.08 & 0.874 & 0.62 & 0.32 \\\\\nLSTM-QR & 0.875 & 45\\% & 0.88 & 0.06 & 0.794 & 0.68 & 0.25 \\\\\nLightGBM-QR & \\textbf{0.827} & 52\\% & 0.59 & 0.06 & \\textbf{0.777} & 0.66 & 0.28 \\\\\nEnsemble & 0.851 & \\textbf{61\\%} & \\textbf{0.48} & 0.08 & 0.810 & \\textbf{0.55} & 0.31 \\\\\nQW-Ensemble & \\textbf{0.827} & 52\\% & 0.59 & 0.06 & \\textbf{0.777} & 0.66 & 0.28 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\subsection{Explainability and ablation}\n\nThe tail forecasts relied mainly on intraday range information (Figure~\\ref{fig:9}). Permuting the range and OHLC features together increased the 5\\% pinball loss by 7.6\\%, far more than any other family: calendar and class 2.2\\%, volatility 1.2\\%, moments and technical indicators 1.1\\%, returns and momentum 0.7\\%, macro 0.5\\% and cross-asset features 0.3\\%. TreeSHAP ranked the current intraday range second for the 5\\% quantile. One discrepancy deserves mention: CPI inflation ranked first by mean $|$SHAP$|$ in fold 5 (2022--2024), but permuting the whole macro family changed the loss by only 0.5\\%. Inflation was high throughout this fold, so the feature is more likely to act as a marker of the period than as a causal driver. Importance rankings were stable between adjacent folds (Spearman correlation 0.63--0.86) and less so between distant ones (0.56 between folds 1 and 5), so the drivers of tail risk shifted gradually over two decades.\n\n\\begin{figure}[!t]\n\\begin{center}\n\\includegraphics[width=\\textwidth]{fig9_xai}\n\\end{center}\n\\caption{Explainability of the LightGBM tail forecasts. \\textbf{(A)} Share of mean $|$TreeSHAP$|$ by feature family for the 5\\%, 50\\% and 95\\% quantile models (fold 5). \\textbf{(B)} Increase in the 5\\% pinball loss when each feature family is permuted (mean and standard deviation of three repeats). \\textbf{(C)} Spearman correlation of feature-importance ranks across the five CV folds.}\\label{fig:9}\n\\end{figure}\n\nAn ablation added the geopolitical risk index to LightGBM, as a 7-day mean and its change relative to a 90-day mean, both lagged. Paper \\#05 of our review had found geopolitical events to be important predictors of downside risk for a single stock \\citep{sigauke2025}. Across 33 assets, the GPR features reduced the pinball loss of the three central quantiles by 0.1\\% (0.2046 against 0.2048; Wilcoxon $p=0.004$ before multiplicity correction) and did not change the Winkler score ($p=0.40$). Once volatility is modelled, the GPR index adds little information for daily return quantiles.\n\n\\section{Discussion}\\label{sec:discussion}\n\n\\subsection{Principal findings}\n\nFour findings stand out. First, evaluation shortcuts that are common in the financial forecasting literature can turn a model with no predictive power into one with an $R^2$ of almost 50\\%, and price-level metrics cannot distinguish a learned model from the random walk. Second, distributional forecasting succeeds where mean forecasting fails: all learned models beat historical simulation by 3--6\\% in pinball loss, with an online quantile-weighted ensemble best overall. Third, conformal calibration helps most in crises and for the lower tail, and a regime-aware aggregation of calibrators gives the best interval scores and VaR backtests at the one-day horizon, but with small effect sizes and not at five days. Fourth, the economic value of better forecasts lies in risk control rather than in excess returns.\n\n\\subsection{Why validation matters more than the model}\n\nThe leakage audit puts the size of model differences into perspective. The best and worst learned models differed by about two percentage points in pinball skill, while the protocol changed the $R^2$ by almost fifty. Centred smoothing is not an exotic error: wavelet denoising, empirical mode decomposition and moving-average filters are often applied to the whole price series before splitting, and every feature derived from such a series contains future information. Shuffled cross-validation is subtler, because for one-day targets it inflated accuracy only slightly; the effect appeared at five days, where overlapping targets link neighbouring observations. Both shortcuts would also inflate the accuracy of the models reviewed in the introduction \\citep{staffini2022,omar2022,yang2025}. We therefore recommend that financial forecasting studies report the random walk, use returns rather than prices, split chronologically before any transformation, purge overlapping labels and document a leakage test.\n\n\\subsection{When does regime information help calibration?}\n\nThe first regime-aware method we tried, which pooled thresholds within regime groups, did not beat ACI, and fourteen further variants of a single calibrator showed that adding regime structure to the thresholds of volatility-adaptive forecasters is largely redundant: the standardisation by $\\sigma_t$ and the volatility features already capture most of the regime. RA-AgCI uses regime information differently, to decide which calibrator to trust, and this was more successful. It never lost to global aggregation at one day, and its advantage was largest on the stock tier when the base model was GARCH or historical simulation. The pattern across bases is informative. Historical simulation does not adapt to volatility, so its errors depend strongly on the regime, and RA-AgCI reduced its Winkler score by 2--6\\% relative to single calibrators (and by 0.1\\% relative to global aggregation). GARCH adapts to volatility but not to other changes, and gained 0.1--0.7\\%. LightGBM already uses range, volatility and cross-asset features, and gained nothing; on stocks it lost slightly. Regime-aware calibration is therefore most useful when the forecaster itself is not regime-aware. At five days the method lost to simpler alternatives, because delayed and overlapping feedback split across many groups slows adaptation.\n\n\\subsection{Choosing a calibration method}\n\nFor practitioners the results suggest a simple rule. If per-asset coverage is the priority, for example to satisfy a regulatory backtest at the asset level, ACI is the most reliable choice: it had the smallest per-asset coverage error in every setting. If the interval score and the lower tail matter most, as in VaR forecasting, RA-AgCI or AgACI is preferable at daily horizons, and RA-AgCI should be preferred when the base model is a simple volatility model or historical simulation. Static split CQR should be avoided in non-stationary markets: its constant is fitted in the calibration period and fails when the regime changes, as it did in COVID-19.\n\n\\subsection{Economic interpretation}\n\nVolatility targeting rewards accurate risk forecasts directly, and the learned models halved the tracking error of historical simulation. They did not raise the Sharpe ratio, because more responsive risk forecasts trade more, and the volatility-managed portfolio literature shows that the Sharpe-ratio benefit of volatility timing depends on the asset and the period \\citep{moreira2017}. The absence of reliable directional predictability is consistent with decades of evidence on out-of-sample return prediction \\citep{welch2008,campbell2008}. The value of machine learning in this setting lies in measuring risk, not in predicting returns.\n\n\\subsection{Practical implications}\n\nRisk managers can obtain well-calibrated daily VaR forecasts across asset classes from a pooled gradient-boosted or ensemble model with an online conformal layer, at low computational cost: the full analysis ran in under 16 minutes. Researchers can use the leakage audit, the purged walk-forward design and the reported baselines as a template. Reviewers of forecasting papers can ask for the random-walk benchmark, return-based metrics and evidence that no transformation was fitted on the full series.\n\n\\subsection{Threats to validity}\n\n\\emph{Internal validity.} RA-AgCI was selected after an earlier proposal failed, from 14 calibrator variants and 5 groupings evaluated on folds 1--3. Folds 4--5 and the hold-out had been seen in the first run for other methods, so only the stock tier is a fully independent confirmation, and there the results depended on the base model. The bad-print filter uses the next day's price; it removes data errors rather than creating features, but a real-time system would need vendor corrections instead. LightGBM was tuned on inner validation sets while GARCH and the LSTM used fixed settings, which may favour LightGBM slightly.\n\n\\emph{External validity.} The data come from Yahoo Finance via Kaggle and contain the quote errors reported above. The stock tier includes only current S\\&P~500 constituents with complete price histories, so it is affected by survivorship bias and omits failed firms. Only daily data and horizons of one and five days were studied.\n\n\\emph{Construct validity.} The CRPS was approximated on an eleven-level quantile grid, the expected shortfall from three tail quantiles, and the five-day GARCH quantiles by a Student-$t$ approximation to the sum of daily returns. Crisis windows and the market-stress threshold were defined with full-sample information, but only for evaluation. Macro data are revised after publication, and real-time vintages were not used.\n\n\\emph{Statistical conclusion validity.} Asset-level tests rest on 33 assets in the main tier and 162 in the stock tier. Effects of 0.1--0.9\\% in the Winkler score are statistically significant in many comparisons but small in absolute terms. Results were corrected for multiplicity within families, but not across the many families reported.\n\n\\subsection{Future work}\n\nFour extensions follow. Intraday data would allow realised-volatility features and horizons shorter than a day. Regime groups learned from the data, for example by hidden Markov models, could replace the fixed volatility and stress thresholds. A multi-horizon version of RA-AgCI could share feedback across horizons to overcome the delay at five days. Finally, survivorship-free stock data would strengthen the confirmation tier.\n\n\\section{Conclusion}\\label{sec:conclusion}\n\nWe evaluated probabilistic forecasts of financial returns on 34 assets in four classes over 26 years, with a confirmation tier of 162 stocks, under a protocol that excludes temporal leakage. Evaluation shortcuts changed the apparent accuracy of return forecasts by almost 50 percentage points of $R^2$, far more than any model, and price-level metrics could not separate any model from the random walk. In distribution, every learned model beat historical simulation, and an online quantile-weighted ensemble was best and the only member of the model confidence set. A regime-aware aggregation of conformal calibrators gave the best interval scores and VaR backtests at the one-day horizon and helped most when the base model did not adapt to volatility, but its gains were small, it did not extend to five days, and plain ACI remained the most reliable for per-asset coverage. Better forecasts improved risk control rather than returns. For financial forecasting research, rigorous validation and appropriate baselines are therefore a prerequisite, and the main value of machine learning lies in measuring risk.\n\n\\section*{Abbreviations}\n\nACE, absolute coverage error; ACI, adaptive conformal inference; AgACI, aggregated adaptive conformal inference; BC-ECI, bias-corrected error-quantified conformal inference; CN-Floor, conformal-naive floor; CQR, conformalized quantile regression; CRPS, continuous ranked probability score; CV, cross-validation; DM, Diebold--Mariano; ECI, error-quantified conformal inference; EWA, exponentially weighted averaging; FZ0, Fissler--Ziegel loss (Patton et al. specification); GARCH, generalized autoregressive conditional heteroskedasticity; GPR, geopolitical risk; HAR, heterogeneous autoregressive; HS, historical simulation; LSTM, long short-term memory; MAPE, mean absolute percentage error; MCS, model confidence set; PICP, prediction-interval coverage probability; QR, quantile regression; RA-AgCI, regime-aware aggregated conformal inference; RCT-ECI, regime-conditional tail-specific ECI; SHAP, Shapley additive explanations; TCP, temporal conformal prediction; TS-ECI, tail-specific ECI; VaR, value at risk.\n\n\\section*{Conflict of Interest Statement}\n\nThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n\\section*{Author Contributions}\n\nSKN: conceptualization, methodology, software, formal analysis, writing -- original draft, supervision, project administration. IK: investigation (literature review), validation, writing -- review and editing. PD: investigation (literature review), validation of the financial evaluation, writing -- review and editing. NF: methodology (risk and value-at-risk evaluation), formal analysis, writing -- review and editing. NHA: data curation, visualization, writing -- review and editing. MT: project administration, resources, writing -- review and editing. RR: data curation, investigation, writing -- review and editing. SK: investigation (macroeconomic regime data), validation, writing -- review and editing. SRR: investigation, resources, writing -- review and editing. WDW: validation, writing -- review and editing. All authors contributed to the article and approved the submitted version.\n\n\\section*{Funding}\n\nThe authors declare that no financial support was received for the research, authorship, and publication of this article.\n\n\\section*{Acknowledgments}\n\nThe authors thank the providers of the public datasets used in this study and Kaggle for computing resources.\n\n\\section*{Data Availability Statement}\n\nThe datasets analyzed for this study are publicly available on Kaggle: Global Financial Markets Dataset (\\url{https://www.kaggle.com/datasets/belbino/global-financial-markets-dataset-2010-present}), US Recession Probability Tracker (\\url{https://www.kaggle.com/datasets/belbino/us-recession-probability-tracker-2000-present}), Gold \\& Silver Price vs Geopolitical Risk (\\url{https://www.kaggle.com/datasets/shreyanshdangi/gold-silver-price-vs-geopolitical-risk-19852025}) and S\\&P 500 Stocks (\\url{https://www.kaggle.com/datasets/andrewmvd/sp-500-stocks}). The analysis notebook and all result tables are available from the corresponding author and will be deposited in a public repository upon publication.\n\n\\bibliographystyle{Frontiers-Harvard}\n\\bibliography{references}\n\n\\end{document}\n",
      "tex_filename": "frontiers.tex",
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      "updated_at": "2026-11-06T13:58:05Z",
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