Kolmogorov-Arnold Networks are Radial Basis Function Networks

TL;DR

The paper identifies inefficiencies in Kolmogorov-Arnold Networks arising from B-spline basis computations and domain rescaling during training. It proposes FastKAN, replacing 3rd-order B-spline bases with Gaussian RBFs and applying layer normalization to maintain domain alignment, yielding a simpler and faster implementation with preserved accuracy. Empirical results show FastKAN achieves about a 3.33x speedup on forward calculations and maintains MNIST-level accuracy, supporting the claim that KANs are effectively radial basis function networks with fixed centers. This work enhances the practicality of KANs for high-dimensional function approximation by reducing computational bottlenecks and enabling more scalable models.

Abstract

This short paper is a fast proof-of-concept that the 3-order B-splines used in Kolmogorov-Arnold Networks (KANs) can be well approximated by Gaussian radial basis functions. Doing so leads to FastKAN, a much faster implementation of KAN which is also a radial basis function (RBF) network.

Figures (2)

• Figure 1: Under proper linear transformations, Gaussian RBFs well approximate 3-order B-spline bases with good precision.
• Figure 2: Curves of validation accuracy along training on MNIST.