On energy function for complex-valued neural networks and its applications

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 investigate existence conditions of energy functions for a class of fully connected complex-valued neural networks and propose an energy function, analogous to those of real-valued Hopfield-type neural networks. It is also shown that, similar to the real-valued ones, the energy function enables us to analyze qualitative behaviors of the complex-valued neural networks. We present dynamic properties of the complex-valued neural networks obtained by qualitative analysis using the energy function. A synthesis method of complex-valued associative memories by utilizing the analysis results is also discussed.