A fault-tolerant Hopfield network for storing correlated patterns
Mathukumalli Vidyasagar, V. Ramesh · 2003
The use of Hopfield-type neural networks for storing a set of correlated (i.e. nonorthogonal) bipolar pattern vectors is considered. The sum of outer products is used as the weight matrix even when the patterns are correlated. It is shown that, provided that the correlation is sufficiently small in a precise sense, each of the given patterns is a stable state of the neural network. Each pattern is also attractive, in that each initial state that is sufficiently close to the specified pattern is mapped into that pattern. It is shown that, when the patterns are uncorrelated, the results given reduce exactly to the known results.>