KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis

2026-05-21

AI Summary

This work addresses the challenge that traditional survival analysis methods struggle to model complex interactions between high-dimensional clinical covariates and time, as well as time-dependent effects. To this end, it proposes the first survival analysis framework based on B-spline Kolmogorov–Arnold Networks (KANs). The approach employs a nonparametric conditional hazard function, where a single-layer architecture recovers generalized additive models and deeper architectures automatically capture covariate interactions and dynamic temporal effects, while effectively handling right-censored data. Theoretically, the estimator’s convergence rate depends only on the smoothness of the underlying hazard function, substantially mitigating the curse of dimensionality. Empirical evaluations on six clinical benchmark datasets demonstrate that the proposed model matches or exceeds the performance of existing statistical and deep learning methods.

Abstract

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.

Problem

• survival analysis
• right censoring
• time-varying effects
• covariate interactions
• nonparametric estimation

Innovation

• Kolmogorov-Arnold Network
• survival analysis
• nonparametric estimation
• curse of dimensionality
• time-varying effects