Kolmogorov--Arnold stability for discontinuous functions

2026-09-07

AI Summary

研究了多变量不连续和无界函数在隐藏层对抗性重参数化下的Kolmogorov-Arnold表示定理的稳定性，为现代深度学习架构提供理论基础。

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.

Problem

• Kolmogorov--Arnold representation theorem
• adversarial reparameterisations
• discontinuous functions
• unbounded functions

Innovation

• Kolmogorov--Arnold representation theorem
• adversarial reparameterisations
• structural robustness