Sharp upper bounds on perfect retrieval in the Hopfield model

被引：15

作者：

Bovier, A ^{[1
]}

机构：

[1] Weierstrass Inst Angew Anal & Stochast, D-10117 Berlin, Germany

来源：

JOURNAL OF APPLIED PROBABILITY | 1999年 / 36卷 / 03期

关键词：

Hopfield model; storage capacity; gradient dynamics; sequential dynamics;

D O I：

10.1017/S0021900200017708

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a sharp upper bound on the number of patterns that can be stored in the Hopfield model if the stored patterns are required to be fixed points of the gradient dynamics. We also show corresponding bounds on the one-step convergence of the sequential gradient dynamics. The bounds coincide with the known lower bounds and confirm the heuristic expectations. The proof is based on a crucial idea of Loukianova (1997) using the negative association properties of some random variables arising in the analysis.

引用

页码：941 / 950

页数：10

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