变分科拉莫戈罗夫-阿诺尔德网络
Variational Kolmogorov-Arnold Network
AI总结：
变分科拉莫戈罗夫-阿诺尔德网络通过学习基础函数数量消除手动指定的限制，提升模型性能。
摘要：
变分科拉莫戈罗夫-阿诺尔德网络通过学习基础函数数量消除手动指定的限制，提升模型性能。
英文摘要：
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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