Abstract

Recently, J. J. Hopfield described a simple model for the operation of neural networks. A Hopfield processor consists of a vector-matrix multiplier and a nonlinear feedback. Farhat and Psaltis have proposed an optical implementation of this model and emphasized a natural link between neural processing and optics. In this paper we present a modification of the Hopfield model, a memory composed of M vectors of, respectively, N bits. We define an equivalence class U (M), for each vector V (M). A probe vector is close to the vector V (M) if it is close enough (in the Hamming sense) to one of the shifted versions. The data are reorganized into S classes, class S containing the vectors shifted by S bits. For each class S we define a validation switch, which is a threshold version of the Hopfield energy. It can be shown that by a proper choice of the switch parameters, the latter is on for class S if and only if the probe is close to version S of one of the memories. Assuming the switch is on for class S, if the probe is shifted back by S bits and injected into a Hopfield processor, it will converge to vector V (M).

© 1986 Optical Society of America