On the capacity of the Hopfield associative memory

The capacity of the Hopfield associative memory (HAM) is analyzed by using a statistical approach. By assuming that the memory network in asynchronous update mode evolves in accordance with a stationary Markov process, the capacity and the recall probability of the asymmetric network are numerically calculated. A convergence theorem is contrived which, in contrast with that proposed by Hopfield, ensures not only the convergence behavior of a symmetric connection matrix but also any asymmetric connection matrix. If M prototype memories, each of length N, are chosen at random and independently from the set {-1.1}, the storage capacity for small N is shown to be approximately 0.12N (with an acceptance level of 0.985). As N approaches infinity, the asymptotic capacity of the network is found to be no more than N/4 log N