A Straightforward Mathematical Analysis for the Hopfield Neural Network

Xiangsun Zhang; Hongfeng Li; Xiaodong Wang

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A Straightforward Mathematical Analysis for the Hopfield Neural Network

更新时间：2025-12-08

- A Straightforward Mathematical Analysis for the Hopfield Neural Network
- Acta Electronica Sinica Issue 10, Pages: 10-18(1992)
- 作者机构：
  
  1. 中国科学院应用数学研究所
  2. 中国科学院应用数学研究所北京100080
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：1992
- 稿件说明：
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[1]章祥荪,李宏峰,王晓东.对Hopfield神经网络的直接数学分析(英文)[J].电子学报,1992(10):10-18.

Xiangsun Zhang, Hongfeng Li, Xiaodong Wang. A Straightforward Mathematical Analysis for the Hopfield Neural Network[J]. Acta Electronica Sinica, 1992, (10): 10-18.
[1]章祥荪,李宏峰,王晓东.对Hopfield神经网络的直接数学分析(英文)[J].电子学报,1992(10):10-18. DOI：

Xiangsun Zhang, Hongfeng Li, Xiaodong Wang. A Straightforward Mathematical Analysis for the Hopfield Neural Network[J]. Acta Electronica Sinica, 1992, (10): 10-18. DOI：

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

其中

Abstract

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

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Related Institution

Dept of Electronic Engineering,Shantou University

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Dept of Electronic EngineeringShantou UniversityShantouGuangdong 515063China

School of Information Science and TechnologyZhongshan UniversityGuangzhouGuangdong 510275China

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