The paper introduces non‑reversible anchored Langevin dynamics (NALD) and its reflected variant (NRALD) for sampling target distributions that may be non‑smooth and heavy‑tailed, both in Euclidean space and on constrained domains. By adding a circulation drift through a divergence‑free skew‑symmetric matrix field and a stream potential, the methods preserve the target distribution without needing density derivatives, admit a random‑time‑change representation, and can be applied with normal reflection on bounded domains. The authors demonstrate that breaking reversibility leads to faster convergence to the target distribution, as shown by finite‑time non‑asymptotic analysis, large‑deviations results, and asymptotic variance reduction, with numerical experiments confirming the algorithms’ efficiency.
First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differen...
The paper introduces Reflected Anchored Langevin Dynamics (RALD), a reflected diffusion that can converge to non‑differentiable target distributions on constrained domains. By employing a smooth anchored reference potential and scaling the drift and noise covariance with a state‑dependent factor, the authors derive an Euler‑Maruyama discretization with projection, yielding the Reflected Anchored Langevin Monte Carlo (RALMC) algorithm. Explicit convergence bounds and iteration complexity in the 2‑Wasserstein distance are proven, and numerical experiments confirm the theoretical predictions and empirical performance.
arXiv:2609. 17577v1 Announce Type: cross Abstract: We study Langevin diffusion and Langevin Monte Carlo (LMC) when the target distribution changes over time.
The paper introduces Langevin-Informed Transfer Learning (LITL), a method that recovers target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift via Dirichlet representation learning, enabling kinetic reconstruction and slow-manifold gradient estimation. The authors provide finite-sample guarantees for eigenvalue, eigenfunction, and drift estimation, and demonstrate LITL’s ability to recover physical transition timescales, build kinetic structure from static generative samples, reconstruct spherical symmetries, and steer latent representations in trained neural networks.
We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
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.
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.
arXiv:2601. 08527v3 Announce Type: replace-cross Abstract: We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants.
The paper introduces a new underdamped Langevin system for sampling Gibbs distributions on matrix spaces where the potential energy is neither convex nor globally gradient‑Lipschitz. By employing non‑quadratic kinetic energies, the authors achieve momentum preconditioning that smooths the momentum via a spectral taming of its gradient. They prove that this dynamics preserves the target Gibbs measure, converges exponentially fast in a weighted total variation distance, and that its Euler–Maruyama discretization remains stable with uniform moment bounds over time.
arXiv:2511.12836v2 Announce Type: replace-cross Abstract: Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGL...
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.