3 problems

Krauth–Mézard and Huang et al.'s freezing conjecture. For the asymmetric binary perceptron, typical solutions belong to clusters of vanishing entropy density, and, more strongly, s…

Krauth–Mézard's sharp threshold conjecture. A sharp threshold occurs at $\alpha^*_{\kappa}$: for constraint densities below $\alpha^*_{\kappa}$, solutions exist with high probabili…

Let $L_{N,\alpha}=\frac{1}{N}\sum_{i=1}^{N}\delta_{X_{\mathbf{\sigma},i}}$ be the empirical measure associated with the configurations in the SK perceptron, and let…