LocallyConnected and Small-World Associative Memories

Abstract—The performance of a locally-connected associative memories built from a one-dimensional array of perceptrons with a fixed number of afferent connections per unit is investigated under conditions of increasing network size. The performance profile yields unexpected results, with a peak in performance when the network size is 2 to 3 times the number of connections per unit. This phenomenon is discussed in terms of small-world behavior. A second simulation using similar techniques, but allowing distal connections reveals a performance profile suggesting that the best performance of the network, measured in terms of pattern bits recalled per node, is greatest at low levels of connectivity. Keywords—Associative memory, capacity, local connectivity, sparse connectivity, small-world networ