STABILITY AND STATISTICAL PROPERTIES OF 2ND-ORDER BIDIRECTIONAL ASSOCIATIVE MEMORY

In this paper, a bidirectional associative memory (BAM) model with sec ond-order connections, namely second-order bidirectional associative m emory (SOBAM), is first reviewed, The stability and statistical proper ties of the SOBAM are then examined, We use an example to illustrate t hat the stability of the SOBAM is not guaranteed, For this result, we cannot use the conventional energy approach to estimate its memory cap acity, Thus, we develop the statistical dynamics of the SOBAM, Given t hat a small number of errors appear in the initial input, the dynamics shows how the number of errors varies during recall, We use the dynam ics to estimate the memory capacity, the attraction basin, and the num ber of errors in the retrieved items, Extension of the results to high er-order bidirectional associative memories is also discussed.