Variational Kolmogorov-Arnold Network
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many s…
Out-of-Distribution DetectionBayesian InferenceKAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward
The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires va…
Kolmogorov-Arnold NetworksScalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
Kolmogorov-Arnold Networks (KANs) offer a promising alternative to Multi-Layer Perceptron (MLP) by placing learnable univariate functions on network edges, enhancing interpretability. However, standard KANs lack probabil…
The Kolmogorov-Arnold representation theorem revisited
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold representation decomposes a multivariate fun…
Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks
Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by…
Computational EfficiencyQuantum Machine LearningImage Classification