Year: 2026
Type: article
Abstract: . This article presents an input convex neural network (ICNN) architecture using Kolmogorov–Arnold networks (ICKANs). Two specific networks are presented. The first is based on a low-order, piecewise-linear representation of functions, and a universal approximation theorem is provided. The second is based on cubic splines, for which only numerical results support convergence. We demonstrate through simple tests that these networks perform competitively with classical ICNNs. We then use the networks to solve optimal transport problems that require a convex approximation of functions and demonstrate their effectiveness. Cubic-ICKANs produce results similar to those of ICNNs.
DOI: 10.1137/25m1778626
Authors: Thomas Deschatre, Xavier Warin
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415037040