The paper establishes global convergence guarantees for third‑order Langevin dynamics applied to non‑convex optimization via simulated annealing with fixed friction and decreasing noise. It shows that, under dissipativity, regularity, and low‑temperature functional‑inequality assumptions, a logarithmic cooling schedule drives objective values to the global minimum with a barrier‑controlled kinetic rate, and that polynomially decreasing step sizes preserve this rate for both exact‑force‑integral and midpoint three‑stage discretizations. Numerical experiments on a double‑well problem and high‑dimensional neural‑network objectives demonstrate that third‑order Langevin schemes outperform overdamped Langevin dynamics and, in some cases, the one‑gradient UBU integrator in terms of terminal‑success point estimates and post‑quench test accuracy.
By Yingli Wang, Kelvin Shuangjian Zhang, Lingjiong Zhu
The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
By Wujun Lv, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
arXiv:2608.25279v1 Announce Type: cross
Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...
By Nawaf Bou-Rabee
arXiv:2606. 28808v1 Announce Type: cross Abstract: We study the leading-order fluctuation of stochastic gradient Euler-Maruyama estimators for generalized non-reversible Langevin dynamics.
By Bingye Ni, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
arXiv:2607. 15208v1 Announce Type: cross Abstract: Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased.
By Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed, Jonathan Weare
arXiv:2610.16248v1 Announce Type: cross
Abstract: We study sampling from $\pi(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ is $\alpha$-strongly convex and $\beta$-smooth with condition n...
By Bo Yuan, Wei Guo, Yongxin Chen
arXiv:2609.06196v1 Announce Type: cross
Abstract: We study the computational effort required for global optimization of a smooth, possibly nonconvex objective $\Gamma:\mathbb{R}^d\to\mathbb{R}$. An a...
By Ioannis Kontoyiannis, Sean Meyn
arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.
By Zequn He, Celia Reina
arXiv:2603. 20467v2 Announce Type: replace-cross Abstract: Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties.
By Joanna Zou, Han Cheng Lie, Youssef Marzouk
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
By Pervez Ali, Weihao Dong, Xiaoyu Wang
arXiv:2604. 23952v2 Announce Type: replace-cross Abstract: Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging.
By Ludovico T. Giorgini
arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
By Arthur Bizzi, Olga Fink