Convolutional Kolmogorov-Arnold Networks

TL;DR

Convolutional Kolmogorov-Arnold Networks introduce learnable spline-based activations into convolutional layers, achieving comparable accuracy to traditional CNNs with significantly fewer parameters, thus enhancing efficiency and expressive power.

Contribution

This paper presents a novel convolutional architecture integrating Kolmogorov-Arnold Networks' learnable activations, improving parameter efficiency and model expressiveness over standard CNNs.

Findings

Achieves similar accuracy to CNNs on Fashion-MNIST

Uses up to 50% fewer parameters

Effectively captures complex spatial relationships

Abstract

In this paper, we present Convolutional Kolmogorov-Arnold Networks, a novel architecture that integrates the learnable spline-based activation functions of Kolmogorov-Arnold Networks (KANs) into convolutional layers. By replacing traditional fixed-weight kernels with learnable non-linear functions, Convolutional KANs offer a significant improvement in parameter efficiency and expressive power over standard Convolutional Neural Networks (CNNs). We empirically evaluate Convolutional KANs on the Fashion-MNIST dataset, demonstrating competitive accuracy with up to 50% fewer parameters compared to baseline classic convolutions. This suggests that the KAN Convolution can effectively capture complex spatial relationships with fewer resources, offering a promising alternative for parameter-efficient deep learning models.