Training and Verifying robust Kolmogorov-Arnold Networks

Kolmogorov–Arnold Networks (KANs) offer strong theoretical representationalpower but, like MLPs and CNNs, remain vulnerable to adversarial attacks. Bench-marks on Fashion MNIST and CIFAR10 confirm this susceptibility. We introduceGloroKAN, leveraging KANs’ B-spline structure to approximate local Lipschitzconstants directly in the forward pass, boosting robustness without gradient-basedadversarial 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’ potentialfor robust, interpretable models, further research is needed to realize their fullpromise.