  Recent advances in associative memory design through structured pattern sets
and graph-based inference algorithms have allowed reliable learning and recall
of an exponential number of patterns. 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 associatively
such as hippocampus and olfactory cortex.
  Here we consider associative memories with 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 surprisingly, we show that internal noise actually
improves the performance of the recall phase while the pattern retrieval
capacity remains intact, i.e., 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 functional benefit to
noisy neurons in biological neuronal networks.
