A Synthesis Theory of Stable Equilibrium Solutions for Large Scale Dynamical Neural Networks and Its Application to Associative Memories.

点击翻译按钮获取中文摘要

In this research project, a synthesis theory for dynamical neural networks using the McCullough-Pitts model proposed in 1943 as a simple mathematical model for a brain neuron was studied particularly focussing on their stable equilibrium solutions. In particular, having in mind application of neural networks to associative memories, first a dynamical neural network having a special structure, called a module neural network, was introduced to store primitive information, and its basic behaviors were investigated. Then, by connecting a number of such module neural networks a large scale and its equilibrium solutions were studied.The main results obtained are listed below :1.A method for constructing a module neural network having a given set of vectors as its stable equilibrium solutions, and further a possibility of ajusting the domain of a stable equilibrium solution was discussed.2.A module dynamical neural network, having a special structure, was introduced, and then a method was proposed for constructing a large scale neural network, called a multi-module neural network, by connecting a number of such module neural networks without changing all the equilibrium solutions of the connectied module neural networks.3.To avoid the rapid decrease in the ability of associative memories due to the number of information vectors to be stored approaching the dimension of the information vectors, a generalized dynamical neural network was proposed, and its construction method was discussed.4.A number of computer simulations were performed to evaluate the effectiveness of the theoretical results obtained.