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Fundamental Research on Neural Networks Based on Analysis Techniques for Electronic Circuits

基于电子电路分析技术的神经网络基础研究

基本信息

批准号：
03650279
负责人：
URAHAMA Kiichi
金额：
$ 1.02万
依托单位：
Kyushu Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

项目摘要

This research addressed some problems appearing in the Hopfield network such as the growth of computational time with the scale of the network, its unavailability for real time processing due to production of infeasible solutions, and absence of guarantee for its performance. The following solutions for these problems were developed: (1) The growth of computational time was proved to be attributed to the increase in the stiffness with the scale of networks. A new stiffly-stable numerical algorithm was proposed and its convergence property was investigated. (2) The penalty method employed in the Hopfield network was shown to produce infeasible solutions. A new analog technique using the Lagrange multiplier method instead of the penalty method was developed and an electronic circuit was implemented which executes this new method. An analog method solving Bellman's equation was proposed for the shortest path problem, linear programming solver based on the duality theorem and combinatorial programming solution method employing WTA mechanism were developed. (3) The worst case error of this new method was evaluated theoretically for the maximum cut problem, one of NP-hard combinatorial problems. This evaluation guarantees the new method performs at worst equally well as the conventional algorithms. (4) A new annealing technique was developed for electronic circuits implementing the Hopfield networks. This annealing method has been verified experimentally to raise the performance of the networks.

本研究解决了Hopfield网络中出现的计算时间随着网络规模的增长而增长、由于产生不可行的解而无法进行实时处理、性能得不到保证等问题。研究结果表明：(1)计算时间的增长是由于网络的刚度随网络规模的增大而增加。提出了一种新的刚稳定数值算法，并对其收敛性进行了研究。(2)在Hopfield网络中使用的惩罚方法产生了不可行解。提出了一种用拉格朗日乘子法代替罚法的模拟技术，并实现了实现该方法的电子电路。提出了求解最短路径问题Bellman方程的模拟方法，开发了基于对偶定理的线性规划求解器和利用WTA机制的组合规划求解方法。(3)对于NP-hard组合问题中的最大割问题，从理论上评价了该方法的最坏情况误差。这种评估保证了新方法在最坏的情况下与传统算法一样好。(4)为实现Hopfield网络的电子电路开发了一种新的退火技术。该退火方法已通过实验验证，提高了网络的性能。