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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{dzhenzher2026kolmogorovarnold,
  title = {{Kolmogorov--Arnold stability for discontinuous functions}},
  author = {Sviatoslav V. Dzhenzher},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07240},
  eprint = {2609.07240},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07240},
}
RIS
TY  - UNPB
TI  - Kolmogorov--Arnold stability for discontinuous functions
AU  - Sviatoslav V. Dzhenzher
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07240
UR  - https://arxiv.org/abs/2609.07240
AB  - 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.
ER  -