Information storage in Hopfield model with reduced complexity

We developed a dynamic neural network with block triangular interconnection weight matrix for associative memory designs. This model has equivalent storage capacity as a fully connected network. In other words, we show the following: For a Hopfield neural network, (x) over dot = -x + Wy + I, y = f(x), vector pattern set E-p(q) = {y(1), y(2), ..., y(q)}, y(i) is an element of R-p, 1 less than or equal to i less than or equal to q, can be stored with [GRAPHICS] and the dimension of (W) over bar(1) depends on the rank of the subsets of E-p(q). The storage capacity of the block triangular structure is justified with the equilibrium requirement as well as the stability condition. This technique is useful in dealing with larger new storage problem while retaining the original architecture. (C) 1998 Elsevier Science Inc. All rights reserved.