Abstract

Abstract-A model of associative memory incorporating global linearity and pointwise nonlinearities in a state space of n-dimensional binary vectors is considered. Attention is focused on the ability to store a prescribed set of state vectors as attractors within the model. Within the framework of such associative nets, a specific strategy for information storage that utilizes the spectrum of a linear operator is considered in some detail. Comparisons are made between this spectral strategy and a prior proposed scheme which utilizes the sum of Kronecker outer products of the prescribed set of state vectors which are to function nominally as memories. The storage capacity of the spectral strategy is linear in n, the dimension of the state space under consideration, while an asymptotic result of n/4logn holds for the storage capacity of the outer product scheme. Computer-simulated results are quoted in suppod of the analysis to show that the spectral strategy stores information more efficiently than the outer product scheme. Estimates of the preprocessing costs incurred in the two algorithms are provided, and recursive strategies are developed for their computation. I.

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