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arxiv: 2509.16750 · v3 · submitted 2025-09-20 · 💻 cs.LG

Interpretable Clinical Classification with Kolmogorov-Arnold Networks

Alejandro Almod\'ovar , Patricia A. Apell\'aniz , Alba Garrido , Fernando Fern\'andez-Salvador , Santiago Zazo , Juan Parras This is my paper

Pith reviewed 2026-05-18 14:59 UTC · model grok-4.3

classification 💻 cs.LG
keywords Kolmogorov-Arnold Networksinterpretable machine learningclinical classificationlogistic KANKAAMtabular health datasymbolic representationshealthcare AI
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The pith

Kolmogorov-Arnold Networks match or exceed baseline performance in clinical classification while remaining fully interpretable.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests Kolmogorov-Arnold Networks as transparent alternatives to black-box models for classifying tabular health data. It introduces Logistic KAN, a flexible extension of logistic regression, and KAAM, an additive model that breaks predictions into per-feature contributions. Across multiple public clinical datasets the new models reach accuracy and other metrics that match or surpass linear, tree-based, and neural baselines, with Logistic KAN achieving the highest overall ranking. KAAM further supplies symbolic formulas, patient-level plots, and nearest-patient lookup so each prediction can be inspected directly. The work shows that strong predictive power and clinical transparency can coexist without post-hoc explanation tools.

Core claim

Kolmogorov-Arnold Networks, through the Logistic KAN and Kolmogorov-Arnold Additive Model variants, achieve predictive performance comparable to or exceeding that of standard linear, tree-based, and neural baselines on clinical tabular datasets while delivering full interpretability via symbolic representations, feature-wise decomposability, patient-level visualizations, and nearest-patient retrieval.

What carries the argument

Kolmogorov-Arnold Networks, which learn univariate functions on edges rather than fixed activations, with KAAM enforcing additive feature-wise decomposition to produce explicit symbolic expressions for each prediction.

If this is right

  • Logistic KAN offers a direct, interpretable generalization of logistic regression for clinical tasks.
  • KAAM enables patient-level visualizations and nearest-patient retrieval without additional explanation methods.
  • The models reduce reliance on post-hoc interpretability techniques in healthcare applications.
  • Transparent symbolic outputs support auditable and potentially actionable clinical decision support.
  • Performance parity with black-box models is maintained across multiple public health datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the learned symbolic forms remain stable across new patient cohorts they could suggest previously unnoticed feature relationships for clinical study.
  • Embedding these models in electronic health record systems could allow real-time inspection of why a risk score was assigned.
  • Direct comparisons with other additive interpretable models such as generalized additive models would clarify whether the KAN edge functions provide unique advantages.
  • Prospective trials measuring changes in physician decisions when using the visualizations would test real-world impact.

Load-bearing premise

The symbolic formulas and feature contributions produced by the models are clinically meaningful and actionable for physicians without further expert validation in real workflows.

What would settle it

A review in which practicing clinicians examine the extracted symbolic expressions and visualizations on real patient cases and consistently rate them as medically implausible or unhelpful for decisions would show the interpretability claim does not hold in practice.

Figures

Figures reproduced from arXiv: 2509.16750 by Alba Garrido, Alejandro Almod\'ovar, Fernando Fern\'andez-Salvador, Juan Parras, Patricia A. Apell\'aniz, Santiago Zazo.

Figure 1
Figure 1. Figure 1: PDPs for a test patient in the Diabetes-130 dataset using the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Importance plot for the patients in the Diabetes-130 dataset using the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: PRPs for a representative test patient from the Diabetes-130 dataset, showing the individual [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Predicted probabilities for test patients in the Heart dataset using [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Importance of the covariates in the Heart dataset predicted using the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: PRP and PDP for two test patients (A in pink, B in purple) in the Heart dataset. The PRP [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Example of an interactive interface for patient assessment in the Heart dataset. Clinicians [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the proposed Logistic-KAN and KAAM models. In Logistic-KAN, the full input vector (x 1 , . . . , xM) is processed jointly through a KAN with multiple layers. The resulting function f p φ(x) allows for flexible, nonlinear interactions between covariates while retaining interpretability through spline-based components. The output logit is then passed through a sigmoid or softmax activation to p… view at source ↗
read the original abstract

The increasing use of machine learning in clinical decision support has been limited by the lack of transparency of many high-performing models. In clinical settings, predictions must be interpretable, auditable, and actionable. This study investigates Kolmogorov-Arnold Networks (KANs) as intrinsically interpretable alternatives to conventional black-box models for clinical classification of tabular health data, aiming to balance predictive performance with clinically meaningful transparency. We introduce two KAN-based models: the Logistic KAN, a flexible generalization of logistic regression, and the Kolmogorov-Arnold Additive Model (KAAM), an additive variant that yields transparent symbolic representations through feature-wise decomposability. Both models are evaluated on multiple public clinical datasets and compared with standard linear, tree-based, and neural baselines. Across all datasets, the proposed models achieve predictive performance comparable to or exceeding that of commonly used baselines while remaining fully interpretable. Logistic-KAN obtains the highest overall ranking across evaluation metrics, with a mean reciprocal rank of 0.76, indicating consistently strong performance across tasks. KAAM provides competitive accuracy while offering enhanced transparency through feature-wise decomposability, patient-level visualizations, and nearest-patient retrieval, enabling direct inspection of individual predictions. KAN-based models provide a practical and trustworthy alternative to black-box models for clinical classification, offering a strong balance between predictive performance and interpretability for clinical decision support. By enabling transparent, patient-level reasoning and clinically actionable insights, the proposed models represent a promising step toward trustworthy AI in healthcare (code: https://github.com/Patricia-A-Apellaniz/classification_with_kans).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Logistic KAN (a flexible generalization of logistic regression) and Kolmogorov-Arnold Additive Model (KAAM, an additive variant yielding feature-wise decomposable symbolic representations) as intrinsically interpretable models for clinical classification on tabular health data. It evaluates both against linear, tree-based, and neural baselines on multiple public datasets, claiming comparable or superior predictive performance (with Logistic-KAN achieving the highest mean reciprocal rank of 0.76) while providing transparency via symbolic formulas, patient-level visualizations, and nearest-patient retrieval, positioning them as practical alternatives for trustworthy clinical decision support.

Significance. If the performance parity and interpretability claims hold under rigorous controls, the work offers a concrete step toward balancing accuracy and transparency in healthcare ML, with the public code release supporting reproducibility. The emphasis on feature-wise decomposability and visualizations addresses a key barrier to adoption of ML in clinical settings, though the clinical actionability of the outputs remains unverified.

major comments (2)
  1. [Abstract and §5] Abstract and §5 (Discussion/Conclusion): The central claim that the models enable 'clinically actionable insights' and represent 'a promising step toward trustworthy AI in healthcare' rests on an untested translation from mathematical decomposability to clinical utility. No physician review, usability study, or workflow integration test is reported to confirm that the KAAM symbolic representations or Logistic-KAN univariate functions would be trusted or used in real decision support, which directly undermines the paper's motivation and conclusions.
  2. [§3 and §4] §3 (Methods) and §4 (Results): Insufficient detail is provided on hyperparameter search procedures, statistical significance testing across runs, and explicit handling of class imbalance or missing data. These omissions make it difficult to assess whether the reported performance advantages (or parity) are robust, which is load-bearing for the claim of consistent outperformance or parity across datasets.
minor comments (2)
  1. [Figures] Figure captions and axis labels in the visualization sections could be expanded to explicitly link the plotted univariate functions or symbolic terms back to the original clinical feature names for easier reader interpretation.
  2. [§4] The mean reciprocal rank calculation and ranking methodology across metrics and datasets should be described with a small example or pseudocode to improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback, which has prompted us to strengthen the clarity, rigor, and appropriate scoping of our claims. We address each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §5] Abstract and §5 (Discussion/Conclusion): The central claim that the models enable 'clinically actionable insights' and represent 'a promising step toward trustworthy AI in healthcare' rests on an untested translation from mathematical decomposability to clinical utility. No physician review, usability study, or workflow integration test is reported to confirm that the KAAM symbolic representations or Logistic-KAN univariate functions would be trusted or used in real decision support, which directly undermines the paper's motivation and conclusions.

    Authors: We agree that the current wording in the abstract and §5 overstates the immediate clinical utility without supporting evidence from physician review or usability testing. The manuscript demonstrates mathematical decomposability and visualization tools that are designed to enable inspection of predictions, but we did not perform any clinical validation studies. In the revised manuscript we will update the abstract and §5 to state that the models provide interpretable representations with the potential to yield clinically actionable insights, while explicitly noting that empirical validation of trust and workflow integration in real clinical settings remains an important direction for future work. This revision will align the conclusions more closely with the evidence presented. revision: yes

  2. Referee: [§3 and §4] §3 (Methods) and §4 (Results): Insufficient detail is provided on hyperparameter search procedures, statistical significance testing across runs, and explicit handling of class imbalance or missing data. These omissions make it difficult to assess whether the reported performance advantages (or parity) are robust, which is load-bearing for the claim of consistent outperformance or parity across datasets.

    Authors: We accept that greater experimental detail is required to allow readers to evaluate robustness. In the revised §3 we will add a complete description of the hyperparameter search procedure, including the optimization method, search ranges, and final selected values for each model and dataset. We will also report statistical significance testing (e.g., paired Wilcoxon signed-rank tests across multiple random seeds or cross-validation folds with p-values) in §4. Finally, we will explicitly document the preprocessing steps for class imbalance (class-weighted loss) and missing data (imputation strategy) in the methods. These additions will be incorporated without altering the reported performance numbers. revision: yes

Circularity Check

0 steps flagged

No circularity in empirical evaluation or interpretability claims

full rationale

The paper introduces Logistic KAN and KAAM as architectural variants of Kolmogorov-Arnold Networks, then evaluates predictive performance on held-out portions of public clinical datasets using standard metrics and comparisons to linear, tree, and neural baselines. Reported results such as mean reciprocal rank of 0.76 for Logistic-KAN arise directly from training and testing procedures rather than any equation that re-derives accuracy from the fitted parameters themselves. Feature-wise decomposability and patient-level visualizations follow immediately from the additive structure of KAAM by definition of the model, without requiring a separate derivation step that collapses back to the same fitted values. No self-citation chain is invoked to justify uniqueness or to forbid alternatives, and the evaluation remains externally falsifiable through the released code and public data. The central claims therefore remain independent of the inputs they are measured against.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The models rest on the Kolmogorov-Arnold representation theorem as a mathematical foundation and on standard supervised learning assumptions for tabular classification. No new physical entities are postulated. Hyperparameters such as grid size and spline order in the KAN layers are fitted during training but are not load-bearing for the interpretability claim.

free parameters (1)
  • KAN grid size and spline order
    Standard KAN hyperparameters chosen during model selection; affect expressivity but not the core interpretability argument.
axioms (2)
  • standard math Kolmogorov-Arnold representation theorem guarantees that multivariate functions can be expressed as sums of univariate functions.
    Invoked to justify the architectural choice of KANs over conventional MLPs.
  • domain assumption Tabular clinical datasets are representative of the target clinical population for the reported metrics.
    Required for generalizing performance results to real clinical use.

pith-pipeline@v0.9.0 · 5836 in / 1454 out tokens · 32903 ms · 2026-05-18T14:59:15.158176+00:00 · methodology

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Reference graph

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    FUNCTION identify.basic.version "sn-basic.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year archivePrefix primaryClass adsurl adsnote version lab...

    work page 2024

  66. [66]

    write newline

    " write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION ...

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  67. [67]

    sn-nature.bst

    FUNCTION identify.nature.version "sn-nature.bst" " [2024/07/19 v1.1 bibliography style]" * top ENTRY address archive author booktitle chapter edition editor eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url doi volume year archivePrefix primaryClass eid adsurl adsnote version l...

    work page 2024

  68. [68]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

    work page