Hopfield Associative Memory with Quantized Weights

Abstract

The use of binary and multilevel memristors in the hardware neural networks implementation necessitates their weight coefficients quantization. In this paper we investigate the Hopfield network weights quantization influence on its information capacity and resistance to input data distortions. It is shown that, for a weight level number of the order of tens, the quantized weights Hopfield-Hebb network capacitance approximates its continuous weights version capacity. For a Hopfield projection network, similar result can be achieved only for a weight levels number of the order of hundreds. Experiments have shown that: (1) binary memristors should be used in Hopfield-Hebb networks, reduced by zeroing all weights in a given row which moduli are strictly less than the maximum weight in the row; (2) in the Hopfield projection networks with quantized weights, multilevel memristors with a weight levels number significantly more than two should be used, with a specific levels number depending on the stored reference vectors dimension, their particular set and the permissible input data noise level.