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

大规模动态神经网络稳定平衡解的综合理论及其在联想记忆中的应用。

基本信息

批准号：
07650464
负责人：
INABA Hiroshi
金额：
$ 1.47万
依托单位：
Tokyo Denki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

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.

在这个研究项目中，研究了动态神经网络的综合理论，使用 1943 年提出的 McCullough-Pitts 模型作为脑神经元的简单数学模型，特别关注其稳定平衡解。特别是，考虑到神经网络在联想记忆中的应用，首先引入具有特殊结构的动态神经网络（称为模块神经网络）来存储原始信息，并研究其基本行为。然后，通过连接多个这样的大规模模块神经网络及其平衡解进行了研究。得到的主要结果如下： 1.构建以给定向量集作为其稳定平衡解的模块神经网络的方法,并进一步讨论了调整稳定平衡解的域的可能性。2.介绍了一种具有特殊结构的模块动态神经网络,并提出了一种构造大规模神经网络的方法,称为多神经网络。 - 模块神经网络，通过连接多个这样的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数而导致联想记忆能力的迅速下降，提出了一种广义的动态模型提出了神经网络，并对其构建方法进行了讨论。4.通过大量的计算机仿真来评估所获得的理论结果的有效性。