  The Little-Hopfield network is an auto-associative computational model of
neural memory storage and retrieval. This model is known to robustly store
collections of randomly generated binary patterns as stable-states of the
network dynamics. However, the number of binary memories so storable scales
linearly in the number of neurons, and it has been a long-standing open problem
whether robust exponential storage of binary patterns was possible in such a
network memory model. In this note, we design simple families of
Little-Hopfield networks that provably solve this problem affirmatively. As a
byproduct, we produce a set of novel (nonlinear) binary codes with an
efficient, highly parallelizable denoising mechanism.
