让基函数数量自动学习，突破KAN模型手动调参瓶颈
Variational Kolmogorov-Arnold Network
- 将基函数数量设为可学习的隐变量，用变分推断优化
- 18个数据集上性能媲美甚至超越传统KAN，无需手动设置层数
- 适合需要自动调参、追求高鲁棒性的机器学习研究者
Kolmogorov-Arnold网络（KANs）通过单变量基函数的复合表示多变量函数，提供理论基础更扎实的替代方案。但其关键缺陷在于需手动设定每层基函数数量——这一直接影响模型容量和性能的超参数，且最优值在不同任务间难以预测。本文提出InfinityKAN，一种变分推断框架，通过将基函数数量建模为带截断指数先验的潜在变量，引入可微加权函数实现梯度优化。我们证明了变分目标的Lipschitz连续性，确保训练稳定。在涵盖合成数据、图像、表格和图结构的18个数据集上的实验表明，InfinityKAN在无需手动选择每层基函数数量的前提下，性能达到或超过传统KAN。
原文摘要 · Abstract (English)
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.
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