Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning
This work proposes Free-RBF-KAN, a novel Kolmogorov–Arnold Network (KAN) architecture that addresses the high computational cost of conventional B-spline-based KANs and the accuracy–efficiency trade-off in existing RBF-KAN variants. By introducing learnable radial basis functions, adaptive grids, and trainable smoothness parameters, Free-RBF-KAN achieves significantly improved computational efficiency while preserving high expressive power. We establish, for the first time, a general universal approximation theorem for RBF-KANs, providing theoretical grounding for their representational capacity. Empirical evaluations across diverse tasks—including multiscale function approximation, physics-informed learning, and operator learning for partial differential equations—demonstrate that Free-RBF-KAN matches the accuracy of the original KAN while substantially accelerating both training and inference.