Let $\mu(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $\kappa=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start. For total-variation error $\varepsilon$, the expected query counts are $O(\kappa^{1/2}d\,(d\log\kappa+\log\frac1\varepsilon))$ gradient queries for the bouncy particle sampler and $O(\kappa d^{1/4}(d\log\kappa+\log\frac1\varepsilon))$ full-gradient equivalents for Zigzag, where $d$ coordinate-partial queries count as one equivalent.
The Proximal Bouncy Particle Sampler is a new sampler that combines ideas from the proximal sampler and the bouncy particle sampler that returns a sample whose law is $\varepsilon$-close to $\mu$ in total variation distance using gradient queries in expectation.
Fan Chen, Sinho Chewi, Jian-Feng Lu et al.· 0 citations
Let $\pi(\mathrm{d} x)\propto e^{-U(x)}\, \mathrm{d} x$ on $\mathbb{R}^d$, where $U$ is continuously differentiable and $m$-strongly convex with a globally $L$-Lipschitz gradient, $0<m\leq L<\infty$, and $\kappa=L/m$. Fixed-step Metropolis-adjusted Langevin algorithm (MALA) has known warm-start mixing-time upper bounds...
Let $K\subset\mathbb{R}^n$ be an isotropic convex body. We prove that the hit-and-run walk, started from any $M$-warm distribution, reaches total-variation distance $\varepsilon$ from the uniform distribution on $K$ in $O\!\left(n^2\psi_n^{-2}\log^3(M/\varepsilon)\right)$ steps, where $\psi_n^{-1}$ is the Kannan-Lov\'a...
We study the problem of sampling from a continuous density $\pi\propto \exp(-V)$ on $\mathbb R^d$, where $V\in C^2(\mathbb R^d)$ has a $\beta$-Lipschitz gradient and $\pi$ satisfies a logarithmic Sobolev inequality with constant $\alpha^{-1}$, and write $\kappa = \beta/\alpha$. We introduce the Gaussian cloud sampler,...
Fan Chen, Sinho Chewi, Jian-Feng Lu et al.· 0 citations
Let $\mathsf{d}\geq1$, $0<\mathsf{s}<\mathsf{d}$, and $N\geq1$. We prove that the optimal fixed-particle-number constant $\Lambda_N(\mathsf{s},\mathsf{d})$ in the Riesz Lieb--Oxford inequality is attained and that these constants are strictly increasing in $N$. The proof combines grand-canonical concentration--compactn...
For every fixed activity $\lambda>0$, we establish three results for the monomer--dimer model on an $n$-vertex simple graph $G$ with $m\ge1$ edges and maximum degree $\Delta$. 1. Near-linear mixing and sampling. Single-edge Glauber dynamics has mixing time $O_\lambda(m[\log^2 n+\log(1/\varepsilon)])$, giving a near-lin...
Tian-Shun Miao, Yi-Tong Yin· 0 citations
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MIT News · Artificial Intelligence· news.mit.eduOct 23, 2026
Assistant Professor Benjamin Lindquist studies how engineers deliberately injected randomness into early AI, giving rise to deep-learning models that sometimes hallucinate.
