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

arXiv: https://arxiv.org/abs/2605.23082 · HTML: https://mlsanity.com/paper/2605.23082/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 23 of 23)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [Smoothing parameter and model selection for general smooth models](https://mlsanity.com/paper/1511.03864/) (2015)
- [CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis](https://mlsanity.com/paper/2409.04290/) (2024)
- [auton-survival: an Open-Source Package for Regression, Counterfactual Estimation, Evaluation and Phenotyping with Censored Time-to-Event Data](https://mlsanity.com/paper/2204.07276/) (2022)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [Neural Frailty Machine: Beyond proportional hazard assumption in neural survival regressions](https://mlsanity.com/paper/2303.10358/) (2023)
- [Approximation Rates in Besov Norms and Sample-Complexity of Kolmogorov-Arnold Networks with Residual Connections](https://mlsanity.com/paper/2504.15110/) (2025)
- [On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators](https://mlsanity.com/paper/2509.19830/) (2025)
- [Deep Partially Linear Transformation Model for Right-Censored Survival Data](https://mlsanity.com/paper/2412.07611/) (2024)
- [Extending Cox Proportional Hazards Model with Symbolic Non-Linear Log-Risk Functions for Survival Analysis](https://mlsanity.com/paper/2504.04353/) (2025)
- [SurvKAN: A Fully Parametric Survival Model Based on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.02179/) (2026)

## Abstract (arXiv)

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.