Some rigorous results for the Hopfield Model

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.