Year: 2025
Type: preprint
Abstract: Kolmogorov-Arnold Networks (KANs) offer a theoretically grounded alternative to multi-layer perceptrons by representing multivariate functions as compositions of univariate basis functions. However, a critical limitation of KANs is the need to manually specify the number of basis functions per layer -- a hyperparameter that directly controls model capacity and substantially impacts performance, yet whose optimal value varies unpredictably across tasks. We present InfinityKAN, a variational inference framework that eliminates this design choice by learning the number of basis functions during training. Our approach models the basis count as a latent variable with a truncated exponential prior, introducing a differentiable weighting function that enables gradient-based optimization. We establish the Lipschitz continuity of the variational objective, ensuring stable training dynamics. Experiments across 18 datasets spanning synthetic, image, tabular, and graph domains demonstrate that InfinityKAN matches or exceeds the performance of KANs while requiring no manual selection of the number of bases for each layer.
Source: arXiv (Cornell University)
Authors: Alesiani, Francesco, Christiansen, Henrik, Errica, Federico
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948147346
Cites:
Cited by:
Related to: