Information storage in Hopfield model with reduced complexity

Abstract

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 ̇ =−x+Wy+I , y=f( x) , vecto pattern set E p q={ y 1,y 2,…,y q }, y t ϵ R p, ⩽i⩽q , can be sored with W= W 1 W 2 W 3 W 4 ϵ R p×p or W ̄ = W ̄ 1 0 W 3 W 4 ϵ R p×p and the dimension of W 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.