aiqbench analysis
This research establishes a rigorous mathematical foundation for the structural robustness of Kolmogorov-Arnold Networks (KANs) against adversarial reparameterizations in hidden layers. By extending the Kolmogorov-Arnold representation theorem to discontinuous and unbounded functions, the study addresses critical stability concerns for next-generation deep learning architectures. The findings offer essential theoretical guarantees for deploying KANs in environments where input data may exhibit non-smooth or extreme variations.
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.
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.
Machine Learning (cs.LG); Functional Analysis (math.FA)
arXiv:2609.07240 [cs.LG]
(or arXiv:2609.07240v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.07240 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 145 words
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