5 problems

Fix $\b5\in\mathbb{R}$, let $\Sigma_N=\{\pm1\}^N$, and let $M_N=M_N(\b5)$ be the largest integer $M$ for which the Ising perceptron solution set … is nonempty, where…

Unique-solution conjecture. For the model at small $\alpha$, the TAP equations have a unique solution $(\mathbf{m}^\star,\mathbf{n}^\star)$, and $\mathbf{m}^\star$ approximates the…

Let $\alpha_c$ be the critical density, and let $\mathbb{P}_{\mathrm r}$ and $\mathbb{P}_{\mathrm{pl}}$ denote respectively the random and planted models of the symmetric Ising per…

Consider successful learning algorithms for the Ising perceptron and the clusters containing the solutions they find. A cluster has positive entropy density when its size is expone…

Let the Ising perceptron have constraint density below its critical capacity. A cluster is a collection of solutions in the solution space. Krauth–Mézard's conjecture. At all densi…