On Energy Function for Complex-Valued Neural Networks

Abstract

Recently models of neural networks that can deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. In this paper we consider a class of fully connected complex-valued neural networks and discuss existence conditions of energy functions for the networks, analogous to those of real-valued Hopfield type neural networks. Based on the conditions we propose an energy function for the complex-valued neural networks. It is also shown that, similar to the real-valued counterparts, this energy function enables us to analyze qualitative behaviors of the complex-valued neural networks. As an application of the energy function, a synthesizing method of complex-valued associative memories is also discussed.