<title>Two optimal encodings for three-layer BAMs</title>

Abstract

Kosko proposed Bidirectional Associative Memory (BAM) , where pairs of patterns (A , B) are encoded. When one of a pair of patterns is presented, the other is expected to be recalled. Irrespective of the number of pattern-pairs encoded, if dimensions of A and B are n and m respectively, a correlation matrix with (mn) elements is required to encode them; and at least O(rnn) computation-time is required for recalling a pattern. It is believed that for practical applications (mn) is a large number. Moreover, to guarantee correct recalling of every encoded pattern, the correlation matrix may need to be augmented, which will increase the size of the matrix further.To overcome these problems, we propose a Three Layer BAM (TLBAM) and two novel encoding methods that require smaller size correlation-matrices. To encode p-pair of patterns, only p(m + n) elements are necessary. Thus, recalling time is also reduced. For instance, to encode three pattern-pairs from a recent paper (with n = 288, m = 280, and p = 3) a correlation matrix of (288x280 =) 80,640 elements is required. This encoding does not recall all three pairs correctly. Using one augmentation method the modified correlation matrix will have 89,600 elements for correct recall of all three pairs. Another augmentation method requires modified correlation matrix of 81,208 elements. Our novel encodings proposed here require two correlation matrices with only (288 x 3 + 3 x 280 =) 1,704 elements.