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.
| Comments: | Preprint |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2507.02466 [cs.LG] |
| (or arXiv:2507.02466v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2507.02466 arXiv-issued DOI via DataCite |
From: Federico Errica [view email]
[v1]
Thu, 3 Jul 2025 09:24:09 UTC (7,120 KB)
[v2]
Thu, 7 May 2026 13:35:04 UTC (617 KB)
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