Adaptive RBF-KAN uses LOOCV and new kernels to boost KAN efficiency

Researchers Cavoretto, De Rossi, Haider, and Noorizadegan have proposed Adaptive RBF-KAN, a new variant of Kolmogorov-Arnold Networks (KANs) that improves on the FastKAN architecture. While FastKAN replaced computationally expensive B-spline edge functions with Gaussian radial basis functions (RBFs), it used a fixed kernel and shape parameter. The team introduces a broader family of radial basis kernels—including Matérn and Wendland functions—and crucially initializes the kernel shape parameter using leave-one-out cross-validation (LOOCV) before refining it during network training. This is the first integration of LOOCV-based kernel scale estimation with deep KAN training.

Evaluated on several two-dimensional benchmark functions, the adaptive RBF-KAN showed that kernel selection and dynamic shape parameters significantly impact performance. Different kernels excelled on different types of functions: smooth functions, those with discontinuities, and oscillatory patterns all benefited from tailored kernel choices. The authors conclude that combining LOOCV-based initialization with adaptive kernel learning offers a practical strategy for improving RBF-based KAN models, potentially reducing training cost while boosting accuracy.