10 problems

Skewed sampling conjecture. There should be a polynomial-time algorithm that approximately samples uniformly from the set of $\vec{n}$-colorings of $G$ whenever

Consider the coordinate-wise Barker proposal, in which each coordinate is separately accepted or reflected according to the current position and gradient information. Reflection-ef…

Let $h$ be the step size, $d$ the dimension, and $m$ the parameter appearing in the preceding regularity and scaling assumptions. Let SG-UBU denote the stochastic-gradient UBU samp…

Dimension-dependence conjecture. Replacing the random-walk Metropolis--Hastings sampler in each local chain $M_i$ by a proximal sampler or a Metropolis-adjusted Langevin algorithm…

Let overdamped LD denote overdamped Langevin dynamics, and consider samplers beyond it, including Hamiltonian or underdamped LD. Also consider normalizing-constant estimation for c…

HMC convergence conjecture. Theorem should hold for the HMC algorithm as well. The conjecture proposes that the paper's main non-asymptotic convergence result in total variation ex…

Let $J$ be the interaction matrix of an Ising model, with largest and smallest eigenvalues denoted by $\lambda_{\max}(J)$ and $\lambda_{\min}(J)$, respectively. The spectral-gap ha…

KLS conjecture. For every convex body $\mathcal K$ in isotropic position, $C_{\mathcal K}=O(1)$.

Dimensional-dependence conjecture. The dependence on $d_x$ present in the authors' results but absent from the results of Akyildiz is solely due to their bounds controlling the err…

Let $Q$ and $P$ be probability distributions over $\mathbb{R}$ such that the density ratio $dQ/dP$ is unimodal, and let $D_{\mathrm{KL}}(Q\mathbin{\|}P)$ denote their Kullback–Leib…