Hopfield model associative memory with nonzero-diagonal terms in memory matrix

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, the version with nonzero-diagonal elements performs nearly identically to one with zero-diagonal terms, and the dropping of the zero-diagonal requirement is advantageous for optical implementation.