Some rigorous results for the Hopfield Model

2001/10/18 by Leonid Litinskii, L. B. Litinskii, Litinskii, L. B.
Computer Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Neural Networks Stability and Synchronization #Neural Networks and Applications #cond-mat.dis-nn

paper · pdf · doi:10.48550/arxiv.cond-mat/0110364

8 pages, 3 eps-files

arxiv created 2001/10/18 · openalex publication_date 2001/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the Hopfield model with the Hebb connection matrix we investigate the case of p memorized patterns that are distorted copies of the same \it standard. In other words, we try to simulate that learning always takes place by means of repeating presentations of one and the same standard, and the presentations are accompanied by distortions of the standard. We obtain some rigorous results relating to the dependence of the fixed points on external parameters of the problem.

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