Improved KLMC for sampling under various conditions.
problem Stable simulation of kinetic Langevin dynamics under different parameters.
method Revisited synchronous Wasserstein coupling analysis with stochastic exponential Euler discretization.
result Exponential integrator can simulate kinetic Langevin dynamics in the overdamped regime with proper time acceleration.
Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.
problem High-dimensional sampling problems in machine learning.
method Unified approach using large deviations theory to study and accelerate Langevin dynamics variants.
result Efficiency of Langevin dynamics variants demonstrated through numerical experiments.
New method learns dynamics from sparse data using geometric constraints.
problem Learning dynamics from sparse, undersampled data.
method Reformulates inference as a stochastic control problem, using geometry-driven path augmentation.
result Accurately recovers stochastic dynamics from extremely undersampled data.
The paper analyzes convergence of Langevin dynamics with time-dependent metrics.
problem Analyzing convergence of Langevin dynamics with time-dependent metrics.
method Formulated a modified gradient flow of the Kullback-Leibler divergence, selected a time-dependent relative Fisher information functional, and developed a time-dependent Hessian matrix condition.
result Proved convergence conditions for various Langevin dynamics.
Adaptive sampling for multimodal distributions converges faster than classical methods.
problem Sampling from multimodal distributions efficiently.
method Adaptive linear dynamics with adaptive diffusion coefficients and vector fields, interpreted as weighted Wasserstein gradient flows.
result Derivative-free dynamics can achieve significantly faster convergence for nonconvex potentials.
NSGLD improves SGLD for non-convex optimization problems.
problem Optimizing non-convex objectives efficiently.
method Introducing non-reversible SGLD by adding an anti-symmetric matrix to the drift term of the Langevin diffusion.
result NSGLD converges faster to the same stationary distribution with non-asymptotic guarantees.
New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.
problem Bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin samplers.
method Delocalization of bias technique applied to these samplers.
result Control W 2 W_2 W 2 bias with O ( K ) O(\sqrt{K}) O ( K ) integration steps for high-dimensional distributions. OLLA framework efficiently samples from constrained distributions with nonconvex constraints.
problem Sampling from constrained distributions with nonconvex constraints is challenging.
method Overdamped Langevin with Landing (OLLA) framework that handles both equality and inequality constraints.
result OLLA converges exponentially fast to the constrained target density in W 2 W_2 W 2 distance. Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.
problem Stochastic dynamics of rigid inclusions on curved surfaces.
method Cartan's method of moving frames, Hamiltonian equations, intrinsic Langevin equations, Fokker-Planck equation.
result Extracted overdamped equations for accurate simulations of diffusion processes.
We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves ε \varepsilon ε error (in 2-Wasserstein distance) in O ( d / ε ) \mathcal{O}(\sqrt{d}/\varepsilon) O ( d / ε ) steps. This is a significant improv…
We study the problem of sampling from a distribution p ∗ ( x ) ∝ exp ( − U ( x ) ) p^*(x) \propto \exp\left(-U(x)\right) p ∗ ( x ) ∝ exp ( − U ( x ) ) , where the function U U U is L L L -smooth everywhere and m m m -strongly convex outside a ball of radius R R R , but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
Study of diffusion annealed Langevin dynamics for generative models.
problem Theoretical efficiency of score-based diffusion processes.
method Rigorous construction and analysis of diffusion processes with Poincaré and logarithmic Sobolev inequalities.
result Improvement in efficiency of diffusion processes through Poincaré and logarithmic Sobolev inequalities.
Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth Itô diffusions exhibiting fast Wasserstein- 2 2 2 contraction, based on local deviat…
A new method for optimization in probability space using Newton's flows.
problem Optimization in probability space with information metrics.
method Information Newton's flows, including Fisher-Rao and Wasserstein-2 metrics, with Newton's Langevin dynamics and variational methods.
result Effective numerical implementation and convergence results for the proposed method.
A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
Proposes methods to add constraints to neural networks to improve stability and generalization.
problem Improving stability and generalization of neural networks.
method Constraint-based regularization using stochastic gradient Langevin dynamics.
result Constraints help stabilize and improve the robustness of deep neural networks.
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…
Constraints improve deep neural network training by stabilizing and enhancing robustness.
problem Vanishing/exploding gradients and poor weight magnitudes in deep neural networks.
method Weight-constrained stochastic dynamics using Langevin dynamics framework.
result Enhanced exploration of the loss landscape and improved generalization.
Improved Langevin algorithms with prior diffusion achieve dimension-independent convergence for non-log-concave distributions.
problem Understanding the dimension dependency of computational complexity in high-dimensional sampling.
method Investigation of prior diffusion technique for log-Sobolev inequality target distributions.
result Modified Langevin algorithm achieves dimension-independent KL divergence convergence.
New method proves dimension-free convergence for ULD in KL divergence.
problem Polynomial scaling of existing convergence guarantees in high dimensions.
method Refined KL local error framework, focusing on tr(H) instead of d.
result First dimension-free KL divergence bounds for discretized ULD.
New method for LVEBMs using saddle-point optimization and Langevin updates.
problem Expressive generative modeling of latent variables with hidden structure.
method Reformulate LVEBM training as a saddle problem, using Langevin updates and gradient flows.
result Proves existence and convergence of the algorithm under standard assumptions, with improved ELBO bounds.
New method optimizes multiple objectives using particle dynamics and gradient flow.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
New Langevin dynamics samples from entropy-regularized optimal transport.
problem Sampling from entropy-regularized optimal transport.
method Introduced analogous diffusion dynamics constrained to Π ( μ , ν ) Π(μ,ν) Π ( μ , ν ) . result Long-time limit is the unique solution of an entropic optimal transport problem.
A new sampling method estimates scores without training or nested MCMC.
problem Efficient sampling from complex, unnormalised distributions.
method Multiscale averaging in SDEs for score estimation.
result Empirical results show competitive accuracy and efficiency.
Study on Wasserstein distance for numerical approximations of stochastic differential equations.
problem Estimating the Wasserstein distance between stochastic differential equation distributions and their numerical approximations.
method Unified framework for analyzing different integrators and a novel splitting method for underdamped Langevin dynamics.
result A novel splitting method for underdamped Langevin dynamics with optimal complexity.
Diffusion models simulate molecular dynamics with adjustable accuracy.
problem Simulating molecular dynamics with high accuracy and efficiency.
method Diffusion models as Euler-Maruyama integrators for Langevin dynamics, learning forces from static snapshots.
result Diffusion models generate molecular trajectories with temporal correlations similar to MD simulations.
New method reduces variance in random coordinate descent for Langevin Monte Carlo.
problem Efficient sampling from log-concave distributions in high dimensions.
method Introduces RCAD, a variance reduction technique for RCD-LMC.
result RCAD-O-LMC and RCAD-U-LMC converge within the same number of iterations as classical LMC methods, saving computational cost.
Study Langevin Monte Carlo for sampling non-log-concave distributions.
problem Sampling from non-log-concave distributions, especially Gaussian mixtures.
method Discretizations of overdamped Langevin diffusions.
result Numerical simulations compare Langevin Monte Carlo algorithms' performance.
For sampling from a log-concave density, we study implicit integrators resulting from θ θ θ -method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for θ ∈ [ 0 , 1 ] θ\in [0,1] θ ∈ [ 0 , 1 ] and a range of step sizes are established. Ou…
The paper develops methods for sampling from log-concave distributions with constraints.
problem Sampling from log-concave distributions with constraints.
method Randomized midpoint discretization of Langevin diffusions with various projections.
result New convergence guarantees for constrained Langevin algorithms.
New bounds on trajectory safety in training models with Langevin Dynamics.
problem Bounding the probability of a model's trajectory staying away from a designated failure region.
method Analyzes Langevin dynamics on smooth, strongly convex loss landscapes, introducing shape-free and local relaxation bounds.
result The in-set probability relaxes to the static value after a burn-in time of order d, using only the global spectral gap of the loss.
The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.
problem Analyzing biases and asymptotic properties of the randomized midpoint method for Langevin diffusions.
method Characterization of stationary distribution and asymptotic normality for numerical integration.
result The step-size needs to go to zero for the method to be asymptotically unbiased.
New algorithms improve sampling from constrained distributions.
problem Sampling from distributions constrained to convex bodies.
method Penalized Langevin Dynamics and Underdamped Monte Carlo methods.
result Improved convergence rates for constrained sampling problems.
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters of the network toward a local minimum. In this article, we employ alternative "sampling" algorithms (referred to here as "thermodynamic para…
New method accelerates Bayesian imaging using Langevin sampling.
problem Bayesian inference in imaging inverse problems with convex geometry.
method Stochastic relaxed proximal-point iteration targeting posterior distribution.
result Accelerated convergence for κ κ κ -strongly log-concave targets. New methods use transport maps to improve Langevin dynamics for sampling.
problem Sampling high-dimensional, non-Gaussian distributions efficiently.
method Apply transport maps to accelerate Langevin dynamics convergence.
result Discretized processes converge to target distribution with non-asymptotic bounds.
Develops a new model to predict training dynamics of large language models.
problem Lack of mechanistic understanding of training dynamics in large language models.
method A first-principles reduced-order model of training dynamics, predicting group-size invariance and stability thresholds.
result Closed-form model predicts training dynamics with high accuracy and provides new diagnostics.
Unified bounds for random subset generalization error and improved SGD Langevin dynamics.
problem Generalization error bounds for random subsets and stochastic gradient Langevin dynamics.
method Unified framework based on Hellström and Durisi's work, extending bounds for Langevin dynamics.
result Unified and refined bounds for generalization error in stochastic gradient Langevin dynamics.
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used L p L^p L p -convergence and Wasserstein metrics. result Uniform-in-time propagation of chaos proved in both L 2 L^2 L 2 -Wasserstein and relative entropy. Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
Extends Langevin dynamics for constrained domains.
problem Optimization of constrained probability measures.
method Mirror mean-field Langevin dynamics (MMFLD).
result Linear convergence guarantees and propagation of chaos results.
Novel geometry-informed irreversible perturbation accelerates Langevin dynamics convergence.
problem Accelerating convergence of Langevin dynamics for Bayesian computation.
method Geometry-informed irreversible perturbation of Riemannian manifold Langevin dynamics.
result Improves estimation performance over irreversible perturbations that ignore geometry.
Langevin Dynamics speeds up mixing time with manifold hypothesis and multi-scale approach.
problem Langevin Dynamics struggles in high dimensions and nonconvex landscapes.
method Utilizes manifold hypothesis to reduce mixing time and employs multi-scale approach to improve image generation quality.
result Mixing time depends on intrinsic dimension rather than ambient dimension, significantly reducing computational complexity.
We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with n n n component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster conver…
Adaptive Langevin dynamics reduces bias in Bayesian inference with mini-batching.
problem Bias in posterior sampling due to mini-batching in Bayesian inference.
method Adaptive Langevin dynamics with dynamical friction to correct noise.
result Quantified bias in posterior distribution due to mini-batching.
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the W…
Langevin dynamics fails to produce accurate samples even with small score function errors.
problem Robustness of Langevin dynamics to score function errors.
method Analysis of Langevin dynamics and score function errors.
result Langevin dynamics produces a distribution far from the target distribution in TV distance even with small L 2 L^2 L 2 errors in the score function.