Design of Hopfield content-addressable memories

Abstract

In the paper, we design the optimal learning rule for the Hopfield content-addressable memories (CAM) based on three well recognized criteria. After analyzing the real cause of the unsatisfactory performance of the Hebb rule and many other existing learning rules, we show that three criteria actually amount to widely expanding the basin of attraction around each desired attractor. For this, we introduce a concept called by the Hamming-stability. Surprisingly, we And that the Hamming-stability for all desired attractors can be reduced to a moderately expansive linear separability condition at each neuron and thus the well known Rosenblatt's perceptron learning rule is the right one for learning the Hammingstability. Computer experiments were conducted, convincingly shpwing that the proposed perceptron Hamming-stability learning rule did take a good care of three optimal criteria.