Lower bounds on the restitution error in the Hopfield model

• 成果类型: Article
• 署名作者: Loukianova, D
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050081
• 发表日期: 1997
• 页码: 161-176
• 关键词: Neural networks; memory capacity

摘要

This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let m denote the number of stored patterns and N that of neurons, Assuming that m/N --> alpha as N --> infinity we show that for alpha > 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as alpha --> infinity.