7 problems

Let $f$ denote the unique viscosity solution of the infinite-dimensional Hamilton–Jacobi equation governing the enriched free energy, and let $\mathbf{G}_N$ and $\sigma^*$ denote t…

Mutual-information concavity conjecture. The mutual information $I(X_1,X_2;Y_1,Y_2,Y_3)$ is concave in $(T_1,T_2,T_3)$. The conjecture concerns the sensing-time allocation in the t…

Let $\mathcal H \subseteq \mathcal X\to\mathcal Y$ be a VC class of dimension $d$, and let $\mathcal A$ be a proper learning algorithm. For a distribution $\mathcal D$, write…

Mutual-information subadditivity conjecture. The inequality

Let $\mathcal{X}$ be a finite alphabet with $|\mathcal{X}|>2$. For an information-distillation function $\mathrm{ID}_M(|\mathcal{X}|,\beta)$, where $M$ is the number of quantizatio…

Let $({\mathsf{x}},{\mathsf{y}})$ be dependent Rademacher random variables taking values in $\{-1,1\}$, and let … consist of $n$ independent, identically distributed copies. For a…

Let $\bar{I}(\tau)$ and $\hat{I}(\tau)$ denote the two population time-delayed mutual information estimators, and define their difference by … A population is statistically homogen…