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Kolmogorov--Arnold stability for discontinuous functions

arXiv 2609.07240 ↗First posted 7 Sep 2026cs.LG math.FAcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 8 of its 27 references that are in the map. First posted on arXiv 7 Sep 2026.

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References · 8

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  2. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  3. 2024Convolutional Kolmogorov-Arnold Networkscited by 77
  4. 2023On the Kolmogorov neural networkscited by 19
  5. 2024On the Robustness of Kolmogorov-Arnold Networks: An Adversarial Perspectivecited by 11
  6. 2024Addressing common misinterpretations of KART and UAT in neural network literaturecited by 9
  7. 2024The Proof of Kolmogorov-Arnold May Illuminate Neural Network Learningcited by 3
  8. 2025Kolmogorov--Arnold stabilitycited by 3

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