LETTER Communicated by Alessandro Treves Noise Facilitation in Associative Memories of Exponential Capacity

Recent advances in associative memory design through structured pat-tern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy cer-tain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate asso-ciatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a func-tional benefit to noisy neurons in biological neuronal networks.