## Bidirectional Associative Memories (1988)

Venue: | IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS |

Citations: | 155 - 3 self |

### BibTeX

@ARTICLE{Kosko88bidirectionalassociative,

author = {Bart Kosko},

title = {Bidirectional Associative Memories},

journal = {IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS },

year = {1988},

volume = {18},

number = {1},

pages = {49--60}

}

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### OpenURL

### Abstract

Stability and encoding properties of two-layer nonlinear feedback neural networks are examined. Bidirectionality, forward and backard information flow, is introduced in neural nets to produce two-way 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 n-by-p 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 two-pattern 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) n-by- 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...