On the crosstalks in sparsely encoded associative memories

It is common practice to store patterns in associative memories by encoding them into vectors with components having binary values 0, +1 or -1, +1. An encoding scheme is said to be sparse if the number of 0´s or -1´s of the encoding vectors is very large compared to the number of +1´s. An asymptotically sparsely encoded associative memory is considered. Patterns are encoded by vectors with components having the values of -1 or +1. The encoding vectors are random realizations of a sequence of n Bernoulli trials heavily biased toward -1. The encoded patterns are stored in the network according to the Hebbian rule. It is proved that the associated crosstalks are asymptotically Gaussian