Random Iterations of Threshold Networks and Associative Memory

A threshold network that can memorize and retrieve a given set of patterns $X_s $ is presented. A theoretical framework is given to allow expression of this property in terms of the dynamics of the network; the patterns in $X_s $ must be attractive fixed points. We give sufficient conditions for this, using a concept of energy. Scaling laws for the storing capacity of random patterns are provided and tested in the case of random as well as nonrandom patterns, such as the letters of the alphabet.