# Variational Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2507.02466 · HTML: https://mlsanity.com/paper/2507.02466/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [Splitting Steepest Descent for Growing Neural Architectures](https://mlsanity.com/paper/1910.02366/) (2019)
- [Firefly Neural Architecture Descent: a General Approach for Growing Neural Networks](https://mlsanity.com/paper/2102.08574/) (2021)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [Self-Expanding Neural Networks](https://mlsanity.com/paper/2307.04526/) (2023)
- [KANICE: Kolmogorov-Arnold Networks with Interactive Convolutional Elements](https://mlsanity.com/paper/2410.17172/) (2024)
- [Variational Inference for Infinitely Deep Neural Networks](https://mlsanity.com/paper/2209.10091/) (2022)
- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)
- [Incorporating Arbitrary Matrix Group Equivariance into KANs](https://mlsanity.com/paper/2410.00435/) (2024)
- [Geometric Kolmogorov-Arnold Superposition Theorem](https://mlsanity.com/paper/2502.16664/) (2025)

## Built on by (most cited first, 1 of 1)

- [Clifford Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.05977/) (2026)

## Abstract (arXiv)

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.