求解线性不定方程组所展现的BP与Hopfield类型神经网络的学习同质性研究  

Common Nature of Learning in BP and Hopfield-type Neural Networks Solving an Underdetermined System of Linear Equations

作　　者：张雨浓[1] 谭宁[2] 李展[1] 莫锦辉[1] 

机构地区：[1]中山大学信息科学与技术学院,广东广州510275 [2]中山大学软件学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2010年第2期1-7,16,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(60775050);新世纪优秀人才支持计划基金资助项目(NCET-07-0887)

摘　　要：主要针对求解线性不定方程组的两种并行计算神经网络模型(BP和Hopfield类型神经网络)进行了探讨。BP神经网络和Hopfield类型神经网络尽管在起源、网络定义、拓扑结构和学习模式上有较大的不同,但这两类人工神经网络在相同学习率条件下求解线性不定方程组中却可以表现出相同的数学公式、学习本质和计算能力,即学习同质性。此外,分别在零初值、相同但非零初值和不同随机初值三种情况下,针对两类人工神经网络求解线性不定方程组体现出来的学习同质性进行了计算机仿真验证,并证实了两类神经网络算法的有效性。The online solution of underdetermined linear equations is investigated by using two types of artificial neural networks （i. e. , BP and Hopfield-type neural networks）. Although they differ from each other in terms of origins, network definition, structures and learning patterns, the BP and Hopfield-type neural networks could be exploited for solving online such underdetermined linear equations and even possess a common mathematical formulation of learning and common computational abilities. In addition, based on zero initial values, the same but nonzero initial values and different random initial values, computer-simulation and verification results are given. These substantiate well the efficacy and commonness of such two types of neural networks on solving underdetermined linear equations.

关 键 词：不定方程 BP神经网络 HOPFIELD神经网络 学习同质性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]