Characteristics of the Hopfield associative memory utilizing isomorphism relations

Isomorphism relations are utilized to analyze the Hopfield associative memory. When the number of fundamental memories m/spl les/3, it is proved that two Hopfield associative memories are isomorphic if they have the same mutual distances between the fundamental memories. The number of stable states and the synchronous convergence time of a Hopfield associative memory are shown to be less than or equal to 2 to the power 2/sup m-1/ and 4 to the power 2/sup m-1/, respectively, where m/spl ges/1. >