12 problems

Let $A$ be an $N \times M$ sign matrix, and let $\operatorname{\textnormal{\textsc{lr}}}(A)$ denote its list replicability number. List-replicability conjecture. Every $N \times M$…

Let $\Gamma$ be a constraint language, and let $r(n)$ be the logarithm of the number of distinct $n$-variable relations definable by primitive positive formulas over $\Gamma$. Chen's…

Quantum Bohnenblust–Hille conjecture. Fix $d\ge 1$. There exists $C_d>0$, depending only on $d$, such that for all $n\ge 1$ and every degree-at-most-$d$ operator…

Let $\Omega$ be a domain, let $F_i\subseteq\mathbb{R}^{\Omega}$ for $i\in[k]$, and let $F_{\max}$ be their $k$-fold maximum. Logarithmic aggregation conjecture. For some universal…

Let $B ewcommand{\mathbb{R}}{\mathbb{R}}subsetmathbb{R}^d$ be the Euclidean unit ball. For $iin[k]$, let … be collections of bounded affine functions on $B$, and let $F_{\max}$ denot…

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…

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Causal penalty conjecture. The optimal learning rate of the student is strictly less than

Huleihel et al.'s conjecture. In the regime $p\to 1/2$, the optimal learning rate of the student is

Let $C_5$ be the family defined earlier in the source, let $\mathcal F^{*n}$ denote its $n$-fold join, and let $\mathrm{UCS}(\mathcal F)$ be the minimum size of an unlabeled compre…