Capacity of associative memory

It is well known that the second-order Hopfield associative memory has storage capacity of order O(n/log n) This result is proved under the assumption that the stored vectors and probe vector are subject to uniform distributions. Unfortunately, this is not always the case practically. We prove that the capacity drops to order of zero when stored vectors and probe vector have nonuniform distributions. Therefore, it is necessary to explore the influence of these distributions on the capacity. To improve the capacity of associative memory, the high-order Hopfield model was proposed by Psaltis, Park and Hong (1988) whose capacity is rigorously determined in this paper. As an alternative of the Hopfield associative memory, are introduce an s-order polynomial approximation of the projection rule and prove that its storage capacity is higher than that of the Hopfield associative memory with the same implementation complexity