Training and Verifying Robust Kolmogorov-Arnold Networks

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.