The Storage Capacity of Generalized Hopfield Models with Semantically Correlated Patterns

#### M. Lowe

1999, v.5, №1, 1-19

ABSTRACT

We analyze the storage capacity of a variant of the Hopfield model with semantically correlated patterns $\xi_i^{\nu}$ (that is the patterns $\xi^\nu$ themselves are correlated but consist of independent components $\xi_{i}^{\nu}$). We show that there is a class of generalized Hopfield models of neural networks with $N$ neurons that can store $N/{(\gamma \log N)}$ or $\alpha N$ spatially correlated patterns (depending on which notion of storage is used), provided that the correlation comes from a homogeneous Markov chain. The quantities $\gamma$ and $\alpha$ are independent of the correlations such that these generalized Hopfield models may be regarded as the legitimate representative of the standard Hopfield model in the presence of semantically correlated data.

Keywords: Hopfield model,neural networks,storage capacity,Markov chains,largedeviations