Input Convex Kolmogorov Arnold Networks
This work provides an incremental improvement for researchers in machine learning and optimization by offering new convex neural network variants for applications like optimal transport.
The authors tackled the problem of constructing input convex neural networks by proposing two architectures based on Kolmogorov-Arnold networks, achieving competitive performance with classical input convex neural networks on simple tests and demonstrating effectiveness in solving optimal transport problems.
This article presents an input convex neural network architecture using Kolmogorov-Arnold networks (ICKAN). Two specific networks are presented: the first is based on a low-order, linear-by-part, 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 on simple tests that these networks perform competitively with classical input convex neural networks (ICNNs). In a second part, we use the networks to solve some optimal transport problems needing a convex approximation of functions and demonstrate their effectiveness. Comparisons with ICNNs show that cubic ICKANs produce results similar to those of classical ICNNs.