On the storage capacity of Hopfield models with correlated patterns

• 成果类型: Article
• 署名作者: Löwe, M
• 署名单位: University of Bielefeld
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 1216-1250
• 关键词: Neural networks; memory capacity; gibbs-states; Lower bounds; overlap

摘要

We analyze the storage capacity of the Hopfield model with correlated patterns (xi(i)(nu)). We treat both the case of semantically and spatially correlated patterns (i.e., the patterns are either correlated in nu but independent in i or vice versa). We show that the standard Hopfield model of neural networks with N neurons can store N/(gamma logN) or alpha N correlated patterns (depending on which notion of storage is used), provided that the correlation comes from a homogeneous Markov chain. This answers the open question whether the standard Hopfield model can store any increasing number of correlated patterns at all in the affirmative. While our bound on the critical value for alpha decreases with large correlations, the critical gamma behaves differently for the different types of correlations.