Improving Leung´s bidirectional learning rule for associative memories

Leung (1994) introduced a perceptron-like learning rule to enhance the recall performance of bidirectional associative memories (BAMs). He proved that his so-called bidirectional learning scheme always yields a solution within a finite number of learning iterations in case that a solution exists. Unfortunately, in the setting of Leung a solution only exists in case that the training set is strongly linear separable by hyperplanes through the origin. We extend Leung´s approach by considering conditionally strong linear separable sets allowing separating hyperplanes not containing the origin. Moreover, we deal with BAMs, which are generalized by defining so-called dilation and translation parameters enlarging their capacity, while leaving their complexity almost unaffected. The whole approach leads to a generalized bidirectional learning rule which generates BAMs with dilation and translation that perform perfectly on the training set in a case that the latter satisfies the conditionally strong linear separability assumption. Therefore, in the sense of Leung, we conclude with an optimal learning strategy which contains Leung´s initial idea as a special case