Empirical Characterization of Lipschitz Continuity in K-nets with Precomputed Inner Functions

Resumen

The application of the Kolmogorov-Arnold representation theorem (KRT) in neural networks has historically been hindered by the non-smooth nature of its inner functions ($\psi$). While this has led to criticism of the theorem's relevance, the work of Sprecher and later Actor (2018) provided a constructive path forward by developing an algorithm for Lipschitz-continuous universal $\psi$. However, it remained an open question whether a network built upon this base could preserve that regularity after training.