5 problems

Consider asymptotic hypothesis-testing problems between probability measures $\mathbb P$ and $\mathbb Q$. For degree at most $D$, define the low-degree advantage by … Here…

Let $\mathcal{Q}$ and $\mathcal{P}$ be sufficiently nice distributions, and let $\operatorname{Adv}_{\leq D}(\mathcal{Q},\mathcal{P})$ denote the degree-$D$ low-degree advantage fo…

Let $t: \mathbb{N} \to \mathbb{N}$. Consider a “natural” high-dimensional testing problem specified by distributions $\mathbb{P}_N$ and $\mathbb{Q}_N$ on an observation space…

Low-degree likelihood-ratio conjecture. If $\|L_n^{\leq D(n)}\|_{L^2(\mathbb{Q}_n)}$ remains bounded as $n\to\infty$ whenever $D(n)\leq t(n)\cdot\operatorname{polylog}(n)$, then th…

Informal low-degree conjecture. For “nice” distributions $\mathbb{P}_n$ and $\mathbb{Q}_n$, if