Training and Verifying robust Kolmogorov-Arnold Networks

Björn Heiderich, Max-Lion Schumacher, Marco Huber

Keywords: KAN, Kolmogorov-Arnold Network, robustness, adversarial robustness, adversarial training, robustness verification

TL;DR: We benchmark Kolmogorov-Arnold Networks on two datasets, Fashion MNIST and CIFAR10, and propose a new training and robustness verification method.

Abstract:

Kolmogorov–Arnold Networks (KANs) offer strong theoretical representational
power but, like MLPs and CNNs, remain vulnerable to adversarial attacks. Bench-
marks on Fashion MNIST and CIFAR10 confirm this susceptibility. We introduce
GloroKAN, leveraging KANs’ B-spline structure to approximate local Lipschitz
constants directly in the forward pass, boosting robustness without gradient-based
adversarial training and nearing adversarially trained performance. Additionally,
we propose a verification method using algebraic geometry to exploit KANs’
piecewise polynomial nature. While these findings highlight KANs’ potential
for robust, interpretable models, further research is needed to realize their full
promise.

Submission Number: 2