Enhancements of the encoding strategy of a discrete bidirectional associative memory (BAM) reported by B. Kosko (1987) are presented. There are two major concepts in this work: multiple training, which can be guaranteed to achieve recall of a single trained pair under suitable initial conditions of data, and dummy augmentation, which can be guaranteed to achieve recall of all trained pairs if attaching dummy data to the training pairs is allowable. In representative computer simulations, multiple training has been shown to lead to an improvement over the original Kosko strategy for recall of multiple pairs as well. A sufficient condition for a correlation matrix to make the energies of the training pairs be local minima is discussed. The use of multiple training and dummy augmentation concepts are illustrated, and theorems underlying the results are presented.

Necessary and sufficient conditions are derived for the weights of a generalized correlation matrix of a bidirectional associative memory (BAM) which guarantee the recall of all training pairs. A linear programming/multiple training (LP/MT) method that determines weights which satisfy the conditions when a solution is feasible is presented. The sequential multiple training (SMT) method is shown to yield integers for the weights, which are multiplicities of the training pairs. Computer simulation results, including capacity comparisons of BAM, LP/MT BAM, and SMT BAM, are presented.

The minimal number of times for using a pair for training to guarantee recall of that pair among a set of training pairs is derived for a bidirectional associative memory.

The multiple training concept first applied to Bidirectional Associative Memory training is applied to the one sweep back-propagation (BP) algorithm. The new algorithm is called Multiple Training Back-Propagation (MTBP). Our computer simulations show that by putting different weights on different pairs in the energy function, this algorithm can increase the training speed of the network. The pair weights are updated during the training phase using Basic Dinerentid Multiplier Method (BDMM). However, those pair weights will not be used during the decoding phase. A sufficient condition for convergence of the training phase is provided, followed by two simulation examples, XOR and stochastic test.