CLuP±Hop approximates Hopfield ground state free energies to within about 0.3% using simple gradient descent, backed by the author's fully lifted random duality theory.
The Hopfield Model with Superlinearly Many Patterns
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abstract
We study the Hopfield model where the ratio $\alpha$ of patterns to sites grows large. We prove that the free energy with inverse temperature $\beta$ and external field $B$ behaves like $\beta\sqrt\alpha+\gamma$, where $\gamma$ is the limiting free energy of the Sherrington-Kirkpatrick model with inverse temperature $\sqrt2\beta$ and external field $B$.
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CLuP practically achieves $\sim 1.77$ positive and $\sim 0.33$ negative Hopfield model ground state free energy
CLuP±Hop approximates Hopfield ground state free energies to within about 0.3% using simple gradient descent, backed by the author's fully lifted random duality theory.