Variational Kolmogorov-Arnold Network

• URL: http://arxiv.org/abs/2507.02466v1
• Date: Thu, 03 Jul 2025 09:24:09 GMT
• Title: Variational Kolmogorov-Arnold Network
• Authors: Francesco Alesiani, Henrik Christiansen, Federico Errica,
• Abstract summary: Kolmogorov Arnold Networks (KANs) are an emerging architecture for building machine learning models.<n>KANs are based on the theoretical foundation of the Kolmogorov-Arnold Theorem and its expansions.
• Score: 10.822246003257563
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kolmogorov Arnold Networks (KANs) are an emerging architecture for building machine learning models. KANs are based on the theoretical foundation of the Kolmogorov-Arnold Theorem and its expansions, which provide an exact representation of a multi-variate continuous bounded function as the composition of a limited number of univariate continuous functions. While such theoretical results are powerful, their use as a representation learning alternative to a multi-layer perceptron (MLP) hinges on the ad-hoc choice of the number of bases modeling each of the univariate functions. In this work, we show how to address this problem by adaptively learning a potentially infinite number of bases for each univariate function during training. We therefore model the problem as a variational inference optimization problem. Our proposal, called InfinityKAN, which uses backpropagation, extends the potential applicability of KANs by treating an important hyperparameter as part of the learning process.

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