离散型 Hopfield 联想存储器k阶吸引子的鲁棒性分析

Robustness analysis of k order attractors in discrete Hopfield associative memory

为对离散型Ｈｏｐｆｉｅｌｄ联想存储器（以下简称为ＤＨＡＭ）平衡点吸引域的鲁棒性进行理论探索，文章基于输入及权值实现误差或扰动同时作用的随机模型，采用统计学方法，推出了ＤＨＡＭ的ｋ阶吸引子（ｋ≥０）鲁棒性的通用计算方法。并针对正交样本经Ｈｅｂｂ规则构成的ＤＨＡＭ，进一步得到了该类网络ｋ阶吸引子鲁棒性的具体计算公式。仿真试验表明所得算法是正确的。讨论了这类ＤＨＡＭ结构及参数等对其ｋ阶吸引子鲁棒性的影响。

The robustness of attractive equilibria which have been stored in Discrete Hopfield Associative Memory (DHAM) is studied. Based on a stochastic model for input and weight implementation errors which may exist simultaneously, a general algorithm is developed to compute the robustness of k order attractors in a given DHAM by using statistical approach. The formula is given to calculate the robustness of k order attractors in DHAM trained by Hebb law upon mutually orthogonal patterns. The simulation results indicate the correctness of the proposed algorithm. The influence of structure and parameters of this kind of DHAM on the robustness of its k order attractors is discussed.