Bidirectional associative memory

Bidirectional associative memory (BAM) is a type of recurrent neural network. BAM was introduced by Bart Kosko in 1988. There are two types of associative memory, auto-associative and hetero-associative. BAM is hetero-associative, meaning given a pattern it can return another pattern which is potentially of a different size. It is similar to the Hopfield network in that they are both forms of associative memory. However, Hopfield nets return patterns of the same size.

A BAM contains two layers of neurons, which we shall denote X and Y. Layers X and Y are fully connected to each other. Once the weights have been established, input into layer X presents the pattern in layer Y, and vice versa.

Imagine we wish to store two associations, A1:B1 and A2:B2.

These are then transformed into the bipolar forms:

From there, we calculate ${\displaystyle M=\sum {\!X_{i}^{T}Y_{i}}}$ where ${\displaystyle X_{i}^{T}}$ denotes the transpose. So,

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