STABILITY, CAPACITY, AND STATISTICAL DYNAMICS OF 2ND-ORDER BIDIRECTIONAL ASSOCIATIVE MEMORY

Bidirectional Associative Memory (BAM) is used for storage of bipolar Library pairs. Second-order BAM is an enhanced version of BAM. The sta bility, capacity and statistical dynamics of second-order BAM are pres ented here. We first use an example to illustrate that the state of se cond-order BAM may converge to limited cycles. When error in the retri eved pairs is not allowed, a lower bound of memory capacity is derived . That is O(min(n(2)/log n, p(2)/log p)), where n and p are the dimens ions of the library pairs. Since the state of second-order BAM may con verge to limited cycles, the conventional method cannot be used to est imate its memory capacity when small errors in the retrieval pairs are allowed. Hence, the statistical dynamics of second-order BAM is intro duced: starting with an initial state close to the library pairs (ther e are some errors in the initial state), how the confidence interval o f the number of errors changes during recalling. From the dynamics, th e attraction basin, memory capacity, and final error in the retrieval pairs can be estimated. Also, some numerical results are given. Finall y, extension of the results to higher-order BAM is discussed.