On the Storage Capacity of the Hopfield Model
- Löwe, Matthias
2010 Mathematics Subject Classification
- 60K40 82C32 82B20
- Hopfield model, neural networks, storage capacity, Markov chains, large deviations
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.