Hopfield associative memories (HAMs) consisting of
n (-1, +1) -binary neurons are considered. Each synaptic connection is assumed to be disconnected with probability
q. Using the Galambos Poison limit theorem of order statistics, it is shown rigorously that HAMs with up to
n2q randomly scattered synaptic disconnections have, with high probability, region of attractions of size ρ
n (ρ
n-error-correction capability) provided that they are not loaded with more than (1-2ρ)
2 (1-
q)
n/2log (1-q)
n2 encoded patterns.
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