On the Storage Capacity of the Hopfield Model

We give a review on the rigorous results concerning the storage capacity of the Hopfield model. We distinguish between two different concepts of storage both of them guided by the idea that the retrieval dynamics is a Monte Carlo dynamics (possibly at zero temperature). We recall the results of McEliece et al. [MPRV87] as well as those by Newman [N88] for the storage capacity of the Hopfield model with unbiased i.i.d. patterns and comprehend some recent development concerning the Hopfield model with semantically correlated or biased patterns.