Some Considerations on Multi-layered Neural Networks, Fuzzy Reasoning Networks and Kolmogorov-Arnold Networks

Abstract

Abstract Back-propagation was proposed in 1986 to learn weighs of input for units in the multi-layered neural network. The differential of error function accelerates decrease of error. Back-propagation was applied to fuzzy control rules in 1988 to learn values in the consequent part and parameters of membership functions (in the simplified fuzzy rules). Very recently, April 2024, Kolmogorov-Arnold network was proposed as promising alterna-(breakpoint)tive, which is based on Kolmogorov-Arnold representation theorem and learn parameters of functions by back-propagation. In this paper, we discuss the common and different features and consider the unification of these networks.