Cs. Leung et al., STABILITY, CAPACITY, AND STATISTICAL DYNAMICS OF 2ND-ORDER BIDIRECTIONAL ASSOCIATIVE MEMORY, IEEE transactions on systems, man, and cybernetics, 25(10), 1995, pp. 1414-1424
Citations number
17
Categorie Soggetti
Controlo Theory & Cybernetics","Computer Science Cybernetics","Engineering, Eletrical & Electronic
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.