Langevin
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Related Articles from SNS
Optimizing Irreversible Perturbations of the Unadjusted Langevin Algorithm
Announce Type: new Abstract: Irreversible perturbations accelerate the convergence of Langevin dynamics, breaking detailed balance while preserving the invariant measure. The design of optimal irreversible perturbations has been studied in the continuous-time Gaussian setting, but extensions to non-Gaussian target distributions, and the impact of time discretization on the design of optimal perturbations, have not been well understood. Numerical discretizations of Langevin dynamics introduce...
Neural Langevin Machine: a local asymmetric learning rule can be creative
arXiv:2506.23546v2 Announce Type: replace-cross Abstract: Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points can be captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that can be used to find them for generative learning of a real dataset. We call this type of generative model a neural Langevin machine, which derives an asymmetric and firing-rate-speed adjusted learning rule requiring only local...
Unbiased estimation of squared concentration in the Fisher-von Mises-Langevin distribution and the impossibility of unbiased concentration
Announce Type: cross Abstract: The estimation of concentration parameter in Fisher-von Mises-Langevin distribution is the directional statistics analogue of the estimation of the precision matrix for the Gaussian distribution. In this work we show that unbiased estimation of this parameter is impossible. With this realization in hand, we provide an alternative parameterization of the Fisher-von Mises-Langevin distribution in terms of the squared concentration, which we term the intensity.
Finite-inertia effects in Langevin dynamics of a lopsided elastic dumbbell using exponential-time differencing schemes
arXiv:2605.31078v1 Announce Type: cross Abstract: Inertia effects in the Langevin dynamics of a lopsided elastic dumbbell are investigated using exponential-time-differencing (ETD) integrators for the corresponding stiff stochastic equations at small mass limit. Starting from the bead-level underdamped Langevin model, we formulate the dynamics in modal coordinates, highlighting two distinct friction scales: an additive friction $\zeta_{\rm trans}=\zeta_1+\zeta_2$ controlling translation...
On the Robustness of Langevin Dynamics to Score Function Error
Announce Type: replace Abstract: We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the $L^2$ errors (more generally $L^p$ errors) in the estimate of the score function. It is well-established that with small $L^2$ errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in...
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
arXiv:2605.31413v1 Announce Type: cross Abstract: We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result shows that the discretization error is governed by an average coordinate-wise smoothness constant, rather than by the usual global smoothness constant. The proof is short and probabilistic, and relies on a refined use of the synchronous coupling.
Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers
arXiv:2601.04791v4 Announce Type: replace Abstract: While latent diffusion models (LDMs) have emerged as powerful priors for inverse problems, existing LDM-based solvers frequently suffer from instability. In this work, we first identify the instability as a discrepancy between the solver dynamics and stable reverse diffusion dynamics learned by the diffusion model, and show that reducing this gap stabilizes the solver. Building on this, we introduce \textit{Measurement-Consistent Langevin...
Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime
Announce Type: replace Abstract: This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The results show that generalization in the low-temperature regime is already signaled by small training errors in the noisier high-temperature regime. The bounds are stable under approximation with Langevin Monte Carlo...
Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning
Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions. For the entropy-regularized RL objective, WPG evolves each state-conditional policy by transporting it along the action gradient of the soft Q-function together with a Langevin-type diffusion. Despite its appeal for continuous-control problems, its global convergence properties remain poorly...
Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems
arXiv:2605.30573v1 Announce Type: new Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities remains a fundamental challenge in machine learning, particularly in black-box settings where gradient information is inaccessible or computationally prohibitive. While Langevin dynamics provides a principled framework for sampling when gradients are accessible, its extension to the black-box settings suffers from high variance and lacks non-asymptotic...