Kolmogorov--Arnold stability for discontinuous functions

arXiv:2609.07240v1 Announce Type: new Abstract: Here we investigate the stability of the Kolmogorov--Arnold representation theorem (KART) under adversarial reparameterisations of the hidden layer for multivariate discontinuous and unbounded functions. Our results provide a rigorous mathematical foundation for the structural robustness of modern deep learning architectures, such as Kolmogorov--Arnold Networks (KANs), under adversarial configurations.

Source: arXiv cs.LG | 2026-09-09