Kernel-KAN: Kernel Kolmogorov Arnold Networks

Abstract

The precise approximation of complex nonlinear functions poses a significant challenge in numerous scientific and engineering fields. Conventional neural network architectures, such as Multi-Layer Perceptrons (MLPs), frequently encounter difficulties in effectively capturing the intricate patterns and irregularities found in high-dimensional functions. This paper introduces the Kernel Kolmogorov-Arnold Network (Kernel-KAN), a novel neural network architecture inspired by the Kolmogorov-Arnold representation theorem, which integrates the robust approximation capabilities of kernel regression. By employing learnable functions that are parameterized by kernel interpolation formulas on the edges of the network, Kernel-KANs improve flexibility, efficiency, and interpretability in function approximation tasks. We showcase the effectiveness of Kernel-KANs through experiments involving digit classification, synthetic function approximation, and multivariate function approximation, demonstrating their superiority over traditional MLPs regarding parameter efficiency and interpretability.