C++ Neural Networks and Fuzzy Logic: Preface

Weights and Training

BAM does not modify weights during its operation, and as mentioned in Chapter 6, like the Hopfield network,

uses one−shot training. The adaptive variety of BAM, called the Adaptive Bidirectional Associative Memory,

(ABAM) undergoes supervised iterative training. BAM needs some exemplar pairs of vectors. The pairs used

as exemplars are those that require heteroassociation. The weight matrix, there are two, but one is just the

transpose of the other as already mentioned, is constructed in terms of the exemplar vector pairs.

The use of exemplar vectors is a one−shot learning—to determine what the weights should be. Once weights

are so determined, and an input vector is presented, a potentially associated vector is output. It is taken as

input in the opposite direction, and its potentially associated vector is obtained back at the input layer. If the

last vector found is the same as what is originally input, then there is resonance. Suppose the vector B is

obtained at one end, as a result of C being input at the other end. If B in turn is input during the next cycle of

operation at the end where it was obtained, and produces C at the opposite end, then you have a pair of

heteroassociated vectors. This is what is basically happening in a BAM neural network.

NOTE:  The BAM and Hopfield memories are closely related. You can think of the

Hopfield memory as a special case of the BAM.

What follow are the equations for the determination of the weight matrix, when the k pairs of exemplar

vectors are denoted by ( X