Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling

arXiv:2608.25052 · stat.ML, cs.LG, math.AP, math.PR · Submitted 2026-08-25 · Read on arXiv

stat.ML, cs.LG, math.AP, math.PR

Submitted: 2026-08-25

Updated: 2026-08-25

Terminology

• Langevin Dynamics — 26× in this paper · explained in 2 episodes
• Accuracy — 23× in this paper · explained in 1 episode
• alpha — 23× in this paper · explained in 1 episode
• Trace — 21× in this paper · explained in 2 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Spectral Gap — 4× in this paper · explained in 5 episodes
• Wasserstein Distance — 4× in this paper · explained in 4 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• 2-Wasserstein Distance — 2× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Nadia — 1× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks
• Sharp convergence rates for Langevin dynamics in the nonconvex setting
• Sharp hypocoercive convergence estimates for underdamped Langevin dynamics via the modified $L^2$ method
• Generalized EXTRA stochastic gradient Langevin dynamics
• A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
• Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms
• Sampling non-log-concave densities via Hessian-free high-resolution dynamics

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