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

在本研究项目中，使用1943年提出的McCullough-Pitts模型作为脑神经元的简单数学模型，研究了动态神经网络的综合理论，重点研究了其稳定平衡解。特别是，考虑到神经网络在联想记忆中的应用，首先引入了一种具有特殊结构的动态神经网络，称为模块神经网络，用于存储原始信息，并研究了其基本行为。然后，通过连接多个这样的模块神经网络，研究了一个大规模的模型及其平衡解。得到的主要结果如下：1.给出了一种以给定的一组向量作为其稳定平衡解的模块神经网络的构造方法，并进一步讨论了调整稳定平衡解的范围的可能性。2.介绍了一种具有特殊结构的模块动态神经网络，并在此基础上提出了一种构造大规模神经网络的方法，称为多模块神经网络，通过连接多个这样的模块神经网络，在不改变连接的模块神经网络的所有平衡解的情况下。3.为了避免由于要存储的信息向量的数量接近信息向量的维度而导致联想记忆能力的迅速下降，提出了一种广义动态神经网络，并讨论了其构造方法。4.进行了大量的计算机仿真，以评估理论结果的有效性。

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.