Associative memory with self-connected nodes

Abstract

The discrete-valued neural network proposed by Hopfield requires zero-diagonal terms in the memory matrix so that the net evolves toward a local minimum of an energy function. For a version of this model with bipolar nodes and positive terms along the diagonal, the net evolves so that only updates that lower the energy by a sufficient amount are accepted. For a net programmed as an outer-product associative content-addressable memory with randomly coded memories, the version with nonzero-diagonal elements performs nearly identically to one with zero-diagonal terms. The dropping of the zero-diagonal requirement may be advantageous for optical implementation in that it allows the memory to configure as a cascade of an inner product operation and weighted summation operation and does not require explicit update of the connectivity matrix.