8 problems

Noncommutative alpha-geometry conjecture. Suppose $n\geq2$. If $p\in(1,2)$, then $\operatorname{Scal}_p$ is strictly Schur-decreasing; if $p\in(2,+\infty]$, then…

Commutative alpha-geometry conjecture. Suppose $n>2$. If $p\in(1,2)$, then $\operatorname{Scal}_p$ is strictly Schur-decreasing; if $p\in(2,+\infty]$, then $\operatorname{Scal}_p$…

Petz's conjecture. The scalar curvature of the BKM metric is a Schur-increasing function; equivalently,

Let $\Theta$ be the neural tangent kernel of a diffusion model and let $k_H$ denote the Hellinger kernel of its data distribution. A Hellinger kernel is understood here as the uniq…

Let a bitnet be a binary Bayesian network equipped with its Fisher information metric, and let $\langle R\rangle$ denote its volume-averaged Ricci scalar. Rodríguez's conjecture. F…

Boundary information inequality conjecture.

Product decomposition conjecture. Given $\mu\in\mathrm{Dens}({\mathbb T}^n)$, there exist $\eta\in\mathrm{Diff}_{\mathrm{d}x}({\mathbb T}^n)$ and functions…

Let $N$ be the size of the finite sample space and let $k$ be the dimension of an exponential family. For a class $\mathcal{H}$ of exponential families, define … In particular, let…