# Kolmogorov--Arnold stability for discontinuous functions

arXiv: https://arxiv.org/abs/2609.07240 · HTML: https://mlsanity.com/paper/2609.07240/

## 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.

## Builds on (most cited first, 8 of 8)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [On the Kolmogorov neural networks](https://mlsanity.com/paper/2311.00049/) (2023)
- [On the Robustness of Kolmogorov-Arnold Networks: An Adversarial Perspective](https://mlsanity.com/paper/2408.13809/) (2024)
- [Addressing common misinterpretations of KART and UAT in neural network literature](https://mlsanity.com/paper/2408.16389/) (2024)
- [The Proof of Kolmogorov-Arnold May Illuminate Neural Network Learning](https://mlsanity.com/paper/2410.08451/) (2024)
- [Kolmogorov--Arnold stability](https://mlsanity.com/paper/2504.05255/) (2025)

## 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.