对Hopfield神经网络的直接数学分析(英文)  

A Straightforward Mathematical Analysis for the Hopfield Neural Network

作　　者：章祥荪[1] 李宏峰 王晓东 

机构地区：[1]中国科学院应用数学研究所,北京100080

出　　处：《电子学报》1992年第10期10-17,共8页Acta Electronica Sinica

摘　　要：本文不是使用一般常用的统计技术,而是直接采用数学方法对神经网络进行分析,以便对Hopfield网用作CAM时的性质有更进一步的了解.通过引进P个n维存储模式之间的非正交度d的概念,给出了网络的容量,即稳定的存储向量的最大数目,在最坏的情形下是(n+d)/(d+1);而描述收敛盆半径的量,稳定度k,则正比于n-p-(P-1)d且反比于p.本文考察了相关模式和伪模式的概念.关于伪模式,证明了在某种条件下sgn是伪模式。Instead of using statistical nature techniques, which are popular in neural network analysis, straightforward mathematical analysis is developed in this paper to promote understanding of properties of the Hopfield network when it is used as a CAM. By introducing a concept of non-orthogonal degree d of a p-set n-binary stored patterns, the capacity of the network, i. e., the maximum number of stable stored patterns, is (n + d)/(d + 1) in the worst case; and the stability degree k*, a quantity describing the radius of convergence basin, is positively proportional to n - p - (p - 1) d and inversely proportional to p. Concepts of associative pattern and spurious pattern are considered; About spurious patterns, we have provedthat in some special cases sgn () are spurious patterns, where

关 键 词：HOPFIELD网 神经网络 数学分析 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]