Learning noisy patterns in a Hopfield network

Abstract

We study the ability of a Hopfield network with a Hebbian learning rule to extract meaningful information from a noisy environment. We find that the network is able to learn an infinite number of ancestor patterns, having been exposed only to a finite number of noisy versions of each. We have also found that there is a regime where the network recognizes the ancestor patterns very well, while performing very poorly on the noisy patterns to which it had been exposed during the learning stage.