Stability of neural network models under tricky function changes explained
Kolmogorov--Arnold stability for discontinuous functions
Machine Learning
Summary
The paper looks at how certain mathematical ways of representing complicated functions stay reliable even when facing tricky changes in how parts of the model are set up. This is especially about functions that can jump suddenly or get very large, which are usually hard to work with. The authors focus on a special deep learning design called Kolmogorov–Arnold Networks and show these designs are robust against difficult rearrangements inside the model. Their work helps explain why these networks remain stable and trustworthy in challenging situations.
Kolmogorov–Arnold representation theoremdiscontinuous functionsdeep learningneural networksKolmogorov–Arnold Networksstabilityadversarial reparameterisationmultivariate functionsstructural robustness
Authors
Sviatoslav V. Dzhenzher
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.