Second-order asymmetric BAM design with a maximal basin of attraction

Abstract—Bidirectional associative memory (BAM) general-izes the associative memory (AM) to be capable of performing two-way recalling of pattern pairs. Asymmetric bidirectional associative memory (ABAM) is a variant of BAM relaxed with connection weight symmetry restriction and enjoys a much better performance than a conventional BAM structure. Higher-Order associative memories (HOAMs) are reputed for their higher memory capacity than the first-order counterparts, yet there are few HOAMs design schemes proposed up to date. To this end, we are concerned in this paper with designing a second-order asymmetric bidirectional associative memory (SOABAM) with a maximal basin of attraction, whose extension to a HOABAM is possible and straightforward. First, a necessary and sufficient condition is derived for the connection weight matrix of SOABAM that can guarantee the recall of all prototype pattern pairs. To respect the complete recall theorem, an adaptive local training rule, which is adaptive in the learning step size and updates only the entries in the connection weight related to the most needful bit of a prototype, is formulated and it leads to better results and faster design. Then derived is a theorem, designing a SOABAM further enlarging the quantities required to meet the complete recall theorem will enhance the capability of evolving a noisy pattern to converge to its association pattern vector without error. Based on this theorem, our algorithm is also modified to ensure each training pattern is stored with a basin of attraction as large as possible. Computer simulations over the color graphics adapter (CGA) fonts have demonstrated the superiority of the proposed local training rule over other prevailing BAM schemes. Index Terms—Asymmetric BAM, basin of attraction, Hebbian learning, second-order associative memory. I