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。

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07650464/
• 关键词: module neural network; stable equilibrium solution; associative memory; multi-module network; dynamical system; 動的ニューラルネットワーク; 引き込み領域; マルチモジュールニューラルネットワーク; 結合係数行列; しきい値ベクトル; 一般化動的ニューラルネットワーク; システム理論

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.

在本研究项目中，使用1943年提出的McCullough-Pitts模型作为大脑神经元的简单数学模型，研究了动态神经网络的合成理论，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，以存储原始信息，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.给出了一种以给定向量集作为稳定平衡解的模块神经网络的构造方法，并讨论了调整稳定平衡解的取值范围的可能性2.介绍了一种具有特殊结构的模块动态神经网络，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而不改变所连接的模块神经网络的所有平衡解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的关联存储器的能力的快速降低，提出了一种广义动态神经网络，并讨论了它的构造方法。4.通过计算机仿真验证了理论结果的有效性。

项目成果

Y.Shoji: "A module neural networks and its basic behaviors" Proc. IEEE Int. Conf. Neural Networks. (1997)

Y.Shoji：“模块神经网络及其基本行为”Proc。

H.Inaba: "Multi-module neural networks and their application to associative memories" Proc. IEEE Int. Conf. Neural Networks and Signal Processing. 1. 110-113 (1995)

H.Inaba：“多模块神经网络及其在联想记忆中的应用”Proc。

Y.Shoji and H.Inaba: "A Module Neural Networks and Its Basic Behaviors" Proc.Int.Conf.Neural Networks. (1997)

Y.Shoji 和 H.Inaba：“模块神经网络及其基本行为”Proc.Int.Conf.Neural Networks。

H.Inaba: "Equilibrium solutions of neural networks with a special structure" Proc.IEEE Int.Conf.Neural Networks and Signal Processing. Vol.1. 75-78 (1995)

H.Inaba：“具有特殊结构的神经网络的平衡解”Proc.IEEE Int.Conf.神经网络和信号处理。

H.Inaba: "Equilibrium solutions of neural networks with a special structure" Proc. IEEE Int. Conf. Neural Networks and Signal Processing. 1. 75-78 (1995)

H.Inaba：“具有特殊结构的神经网络的平衡解”Proc。