Complex-valued Hopfield neural networks with real weights in synchronous mode

Abstract

A complex-valued Hopfield neural network with a multistate activation function converges in asynchronous mode, whereas it converges or is trapped at a cycle of length two in synchronous mode. For parallel processing, convergence in synchronous mode is necessary. In particular, a complex-valued Hopfield neural network (CHNN) is the most widely used multistate Hopfield model, and it is desirable that a CHNN converges in synchronous mode. In this work, a real-weight CHNN (RWCHNN) is proposed. An RWCHNN restricts the weights of a CHNN to real numbers and has half weight parameters of a CHNN. We provide the stability conditions of an RWCHNN in synchronous mode and prove that the projection rule satisfies them. The RWCHNN is the first model such that it converges in synchronous mode and has half weight parameters of a CHNN. Computer simulations show that the average update count until convergence is far less than those of the hypercomplex-valued Hopfield neural networks with the same number of weight parameters of an RWCHNN.