Convergence Analysis of Caputo-Type Fractional Order Complex-Valued Neural Networks

Abstract

The complex-valued neural networks are the class of networks that solve complex problems by using complex-valued variables. The gradient descent method is one of the popular algorithms to train complex-valued neural networks. Essentially, the established networks are integer-order models. Compared with classical integer-order models, the built models in terms of fractional calculus possess significant advantages on both memory storage and hereditary characteristics. As one of commonly used fractional-order derivatives, Caputo derivative is more applicable in practical problems due to its simple requirements on initial condition. In this paper, we adopt this specific fractional-order derivative to train split-complex neural networks. As a result, the monotonicity and weak convergence of the presented model are rigorously proved. In addition, numerical simulation has effectively verified its competitive performance and also illustrated the theoretical results.