The Hopfield Model with Superlinearly Many Patterns

We study the Hopfield model where the ratio $α$ of patterns to sites grows large. We prove that the free energy with inverse temperature $β$ and external field $B$ behaves like $β\sqrtα+γ$, where $γ$ is the limiting free energy of the Sherrington-Kirkpatrick model with inverse temperature $\sqrt2β$ and external field $B$.

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