Variational Kolmogorov-Arnold Network

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.

@article{alesiani2025_2507.02466,
  title={ Variational Kolmogorov-Arnold Network },
  author={ Francesco Alesiani and Henrik Christiansen and Federico Errica },
  journal={arXiv preprint arXiv:2507.02466},
  year={ 2025 }
}