Bidirectional associative memories

TLDR

Bidirectionality in neural nets enables two-way associative search, and the bidirectional associative memory (BAM) is the minimal two-layer nonlinear feedback network. The study examines the stability and encoding properties of two-layer nonlinear feedback neural networks. The BAM, a minimal two-layer nonlinear feedback network, encodes heteroassociative information by summing correlation matrices and, upon activation, quickly converges to a stable two-pattern reverberation state. The author proves that any n-by-p matrix defines a bidirectionally stable heteroassociative memory for binary/bipolar and continuous neurons, that stable reverberation is a local energy minimum, that storage capacity is roughly m<min(n,p), and that bipolar coding outperforms binary coding on average.

Abstract

Stability and encoding properties of two-layer nonlinear feedback neural networks are examined. Bidirectionality is introduced in neural nets to produce two-way associative search for stored associations. The bidirectional associative memory (BAM) is the minimal two-layer nonlinear feedback network. The author proves that every n-by-p matrix M is a bidirectionally stable heteroassociative content-addressable memory for both binary/bipolar and continuous neurons. When the BAM neutrons are activated, the network quickly evolves to a stable state of two-pattern reverberation, or resonance. The stable reverberation corresponds to a system energy local minimum. Heteroassociative information is encoded in a BAM by summing correlation matrices. The BAM storage capacity for reliable recall is roughly m<min (n,p). It is also shown that it is better on average to use bipolar (-1,1) coding than binary