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arXiv · 2609.07240

Kolmogorov--Arnold stability for discontinuous functions

Sviatoslav V. Dzhenzher
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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.

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Sviatoslav V. Dzhenzher. 2026-09-07. Kolmogorov--Arnold stability for discontinuous functions. https://arxiv.org/abs/2609.07240

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