BSRBF-KAN: A combination of B-splines and Radial Basic Functions in Kolmogorov-Arnold Networks

A recent work of Liu et al. [1] over KANs opened a new paradigm in applying learnable activation functions as "edges" to fit training data instead of using fixed ones as "nodes" that are usually used in MLPs. The theory behind KANs relies on the Kolmogorov-Arnold representation theorem (KART), which states that a continuous function of multiple variables can be expressed as a combination of continuous functions of a single variable through additions. KANs are anticipated to bring a fresh perspective to solving issues that have been overshadowed by MLPs. With that inspiration, many scientists have flocked to develop different types of KANs based on popular polynomial and basis functions. While these works focus on univariate functions to set up KANs, none have explored their combination. Therefore, we aim to combine B-splines [2] and Radial Basis Functions [3] to build a combined KAN named BSRBF-KAN.