Associative Memory via a Sparse Recovery Model

An associative memory is a structure learned from a dataset $\mathcal{M}$ of vectors (signals) in a way such that, given a noisy version of one of the vectors as input, the nearest valid vector from $\mathcal{M}$ (nearest neighbor) is provided as output, preferably via a fast iterative algorithm. Traditionally, binary (or $q$-ary) Hopfield neural networks are used to model the above structure. In this paper, for the first time, we propose a model of associative memory based on sparse recovery of signals. Our basic premise is simple. For a dataset, we learn a set of linear constraints that every vector in the dataset must satisfy.