RIGOROUS BOUNDS ON THE STORAGE CAPACITY OF THE DILUTE HOPFIELD MODEL

We study a neural network model consisting of N neurons where a dendritic connection between each pair of neurons exists with probability p and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that if p greater-than-or-equal-to c[(1n N)/N]1/2, the model can store at least m = alpha(c)pN patterns, where alpha(c) almost-equal-to 0.027 if c greater-than-or-equal-to approximately 3 and decreases proportional to 1/(-1n c) for c small. This generalizes the results of Newman for the standard Hopfield model.