外积取等联想记忆神经网络部分同步收敛性

Convergence Analysis of Associative Memory Neural Networks Based on Outer Product Equation Learning Rule in Partially Synchronous Operation Mode

在生物视觉系统中发现的部分同步振荡现象被认为是视觉信息处理的重要机制 ,并对认识脑信息处理机制有重要意义。以联想记忆神经网络为例 ,针对外积取等学习准则定义了两种部分同步运行规则 ,通过引入样本向量割、割等价及割互补的概念 ,对外积取等联想记忆神经网络部分同步运行的收敛性作了直接的数学分析 ,证明了实现收敛所需的迭代数是有限的。

The partially synchronous oscillating phenomenon found in the biological visual systems is thought as the key mechanism of visual information processing, and it is important to understand the mechanism of brain information processing. In this paper, two kinds of partially synchronous operation modes are defined based on outer product equation learning rule of associative memory neural networks. By introducing concepts of cut, cut equivalence and cut complement, straightforward mathematical analysis for the convergence of associative memory neural networks based on outer product equation learning rule in partially synchronous operation mode is given. The following results are proved: the number of iterations required to achieve convergence is finite.