Attraction basin of bidirectional association memories.

Abstract

In this paper, we investigate the attraction basin of the bidirectional associative memory (BAM) model. The BAM is a two-layer heteroassociator that stores a prescribed set of bipolar library pairs. It consists of two layers of neurons. One layer has n neurons and the other has p neurons. We will first point out why the conventional energy approach cannot tell us about the attraction basin of each library pair. We then rigorously derive the statistical dynamics of the BAM, which shows how the upper bound on the number of errors changes during recalling for an arbitrary error pattern in the initial state. From the dynamics, we can estimate the attraction basin for the worst case errors, as well as the memory capacity and the number of errors in the retrieved pairs. The memory capacity is alpha rn, where alpha r (0 < alpha r < 1) depends on the ratio [formula: see text]. The number of errors in the retrieved pairs is [formula: see text] when the number of library pairs is alpha n. When r = 1, the lower bound on the attraction basin for the worst case errors is about 0.0068n.