level: research
kolmogorov-arnold networks (kans) learn univariate edge functions to approximate complex multivariate functions. standard kans use b-spline bases, which can be slow. fastkan speeds this up by using gaussian radial basis functions (rbfs) but keeps a fixed kernel shape. this work introduces adaptive rbf-kan, which uses leave-one-out cross-validation (loocv) to set the shape parameter for each rbf kernel during training. this is the first time loocv-based scale estimation has been combined with deep kan training.
the study also brings matern and wendland kernels into the kan framework for the first time. these kernels offer different smoothness and compact support properties compared to the gaussian kernel. by testing on regression and classification tasks, the authors compare how these kernels perform with and without the loocv initialization. the adaptive approach aims to reduce the need for manual tuning of the shape parameter, which can strongly affect model accuracy.
experiments show that adaptive rbf-kan with loocv initialization often improves performance over fixed-shape fastkan. the matern and wendland kernels provide viable alternatives, with wendland kernels being compactly supported, which can speed up computation. the method keeps the efficiency of rbf-based kans while adding flexibility. the code is available for others to test and build upon.
why it matters: automating kernel shape selection in rbf-based kans can make these networks easier to use and more accurate for function approximation tasks in data science.