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SurvKAN: A Fully Parametric Survival Model Based on Kolmogorov-Arnold Networks

Marina Mastroleo, Alberto Archetti, Federico Mastroleo, Matteo Matteucci

TL;DR

SurvKAN addresses the need for accurate, interpretable time-to-event prediction without relying on the proportional hazards assumption by introducing a fully parametric, time-continuous survival model based on Kolmogorov--Arnold Networks. Time is treated as an explicit input, and the model directly outputs the log-hazard $\log h(t|\mathbf{x})$, enabling end-to-end training on the full likelihood and yielding hazard estimates that vary flexibly over time. Empirical results across ten benchmark datasets show SurvKAN achieving competitive or superior discrimination and calibration relative to Cox-based, neural, and tree-based baselines, while maintaining interpretability through learnable univariate edge functions and potential symbolic regression to closed-form expressions. The approach provides clinically meaningful insights into how features influence risk over time, supporting trust and potential deployment in safety-critical settings where transparency is essential.

Abstract

Accurate prediction of time-to-event outcomes is critical for clinical decision-making, treatment planning, and resource allocation in modern healthcare. While classical survival models such as Cox remain widely adopted in standard practice, they rely on restrictive assumptions, including linear covariate relationships and proportional hazards over time, that often fail to capture real-world clinical dynamics. Recent deep learning approaches like DeepSurv and DeepHit offer improved expressivity but sacrifice interpretability, limiting clinical adoption where trust and transparency are paramount. Hybrid models incorporating Kolmogorov-Arnold Networks (KANs), such as CoxKAN, have begun to address this trade-off but remain constrained by the semi-parametric Cox framework. In this work we introduce SurvKAN, a fully parametric, time-continuous survival model based on KAN architectures that eliminates the proportional hazards constraint. SurvKAN treats time as an explicit input to a KAN that directly predicts the log-hazard function, enabling end-to-end training on the full survival likelihood. Our architecture preserves interpretability through learnable univariate functions that indicate how individual features influence risk over time. Extensive experiments on standard survival benchmarks demonstrate that SurvKAN achieves competitive or superior performance compared to classical and state-of-the-art baselines across concordance and calibration metrics. Additionally, interpretability analyses reveal clinically meaningful patterns that align with medical domain knowledge.

SurvKAN: A Fully Parametric Survival Model Based on Kolmogorov-Arnold Networks

TL;DR

SurvKAN addresses the need for accurate, interpretable time-to-event prediction without relying on the proportional hazards assumption by introducing a fully parametric, time-continuous survival model based on Kolmogorov--Arnold Networks. Time is treated as an explicit input, and the model directly outputs the log-hazard , enabling end-to-end training on the full likelihood and yielding hazard estimates that vary flexibly over time. Empirical results across ten benchmark datasets show SurvKAN achieving competitive or superior discrimination and calibration relative to Cox-based, neural, and tree-based baselines, while maintaining interpretability through learnable univariate edge functions and potential symbolic regression to closed-form expressions. The approach provides clinically meaningful insights into how features influence risk over time, supporting trust and potential deployment in safety-critical settings where transparency is essential.

Abstract

Accurate prediction of time-to-event outcomes is critical for clinical decision-making, treatment planning, and resource allocation in modern healthcare. While classical survival models such as Cox remain widely adopted in standard practice, they rely on restrictive assumptions, including linear covariate relationships and proportional hazards over time, that often fail to capture real-world clinical dynamics. Recent deep learning approaches like DeepSurv and DeepHit offer improved expressivity but sacrifice interpretability, limiting clinical adoption where trust and transparency are paramount. Hybrid models incorporating Kolmogorov-Arnold Networks (KANs), such as CoxKAN, have begun to address this trade-off but remain constrained by the semi-parametric Cox framework. In this work we introduce SurvKAN, a fully parametric, time-continuous survival model based on KAN architectures that eliminates the proportional hazards constraint. SurvKAN treats time as an explicit input to a KAN that directly predicts the log-hazard function, enabling end-to-end training on the full survival likelihood. Our architecture preserves interpretability through learnable univariate functions that indicate how individual features influence risk over time. Extensive experiments on standard survival benchmarks demonstrate that SurvKAN achieves competitive or superior performance compared to classical and state-of-the-art baselines across concordance and calibration metrics. Additionally, interpretability analyses reveal clinically meaningful patterns that align with medical domain knowledge.
Paper Structure (15 sections, 2 equations, 1 figure, 3 tables)

This paper contains 15 sections, 2 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Survival Analysis
  4. Kolmogorov--Arnold Networks
  5. Method
  6. SurvKAN Architecture
  7. Training Procedure
  8. Inference and Interpretability
  9. Experiments
  10. Experimental Setup
  11. Results
  12. Interpretability
  13. The GBSG2 Dataset
  14. The METABRIC Dataset
  15. Conclusion

Figures (1)

  • Figure 1: KAN architecture schema from inputs (bottom) to log-hazard (top) alongside feature-specific hazard contributions in the subsequent rows.