Adaptive Basis Functions for Enhanced Function Approximation in Kolmogorov–Arnold Networks

This paper proposes adaptive basis functions (AdaKANs) for Kolmogorov–Arnold Networks (KANs), a novel addition to KANs that enables optimized adjustment of univariate basis functions during training. KANs, with additional Adaptive Basis Functions (AdaKANs) achieve smoother convergence, improved generalization, and an average reduction in mean-squared error by 50\% on noisy polynomial functions, and 3 benchmark datasets compared to a regular KAN, Fourier Function Networks, and a regular MLP. This method addresses the limitations of static basis functions, further improving the scalability, flexibility, and applicability of KANs in complex function approximation tasks.