Krauth-Mezard Storage Capacity of the Ising Perceptron
Prior state unknown→proved
the last conditional step in the Ding-Sun and Huang bounds is discharged
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probability-statistics / Probability
Krauth-Mezard Storage Capacity of the Ising Perceptron
Krauth and Mezard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant $\alpha_\star \approx 0.8330786$. Ding and Sun proved the matching lower bound and Huang the upper bound, but each was conditional on a global sign condition nobody had verified. Both conditions now hold rigorously, so $M_N/N \to \alpha_\star$ in probability with $\alpha_\star \in [0.833078599, 0.833078600]$.
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Krauth and Mezard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant $\alpha_\star \approx 0.8330786$. Ding and Sun proved the matching lower bound and Huang the upper bound, but each was conditional on a global sign condition nobody had verified. Both conditions now hold rigorously, so $M_N/N \to \alpha_\star$ in probability with $\alpha_\star \in [0.833078599, 0.833078600]$.
the last conditional step in the Ding-Sun and Huang bounds is discharged
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