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Bidirectional Associative Memories
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS
, 1988
"... Stability and encoding properties of twolayer nonlinear feedback neural networks are examined. Bidirectionality, forward and backard information flow, is introduced in neural nets to produce twoway associative search for stored associations (A, B, ). Passing information through M gives one directi ..."
Abstract

Cited by 155 (3 self)
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Stability and encoding properties of twolayer nonlinear feedback neural networks are examined. Bidirectionality, forward and backard information flow, is introduced in neural nets to produce twoway associative search for stored associations (A, B, ). Passing information through M gives one direction; passing it through its transpose M r gives the other. A bidirectional associative memory. (BAM) behaves as a hetero associative content addressable memory (CAM), storing and recalling the vector pairs (A1, Bi),..,(Am Bin) , where .4 {0,1}"and B We prove that every nbyp matrix M is a bidirectionally stable heteroas sociative CAM for both binary/bipolar and continuous neurons a, and hi. When the BAM neurons are activated, the network quickly evolves to a stable state of twopattern reverberation, or resonance. The stable reverberation corresponds to a system energy local minimum. Heteroassociafive inlormation is encoded iu a BAM by summing correlation matrices. The BAM storage capact .ty for reliable recall is roughly m < niin(n, p). No more heteroassociafive pairs can be 'reliably stored and recalled than the lesser of the dimensions of the pattern spaces (0,1 }"and 0,1 } P. The Appendix shos that it is better on average to use bipolar { 1,i} coding than binary. {0,1 } coding of heteroassociative pairs (.4, B,). BAM encoding and decoding are combined in the adaptive BAM, which extends global bidirectional stabflit), to realtime unsupervised learning. Temporal patterns (AE,., A,,) are represented as ordered lists of binary/bipolar vectors and stored in a temporal associative memory (TAM) nby matrix M as a limit cycle of the dynamical system. Forward recall proceeds through M, backward recall through M r . Temporal patterns are stored by summing contiguous bipolar...