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.
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.
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.
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 Lp-convergence and Wasserstein metrics. result Uniform-in-time propagation of chaos proved in both L2-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 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.
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 L2 errors in the score function. A new method uses higher-order Langevin dynamics with critical damping for better generative modeling.
problem Improving generative models using Langevin dynamics with auxiliary variables.
method Introducing higher-order Langevin dynamics with critical damping, providing closed-form solutions.
result Improved generative models with better performance as measured by FID metric.
Adaptive algorithm improves convergence rate of Langevin dynamics.
problem Improving convergence rate of Langevin dynamics.
method Adaptive non-reversible stochastic gradient Langevin dynamics algorithm.
result Improved convergence rate of the algorithm.
Paper improves convergence rate of Langevin Dynamics algorithms.
problem Sampling problems and non-convex optimization in machine learning.
method Stochastic Variance Reduced Gradient Langevin Dynamics and Stochastic Recursive Gradient Langevin Dynamics with improved convergence rates.
result Proves convergence to objective distribution under weaker conditions.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
Study on Langevin dynamics convergence rates and their application to GAN training.
problem Understanding the long-term behavior of Langevin dynamics equations.
method Analytical and numerical methods to study convergence rates of underdamped mean-field Langevin dynamics.
result Exponential convergence rate results for the Langevin dynamics under various conditions.
Paper approximates risk measures using SGD with Langevin dynamics.
problem Approximating arbitrary law invariant risk measures.
method Stochastic Gradient Langevin Dynamics (SGD-Langevin) for general risk measures.
result Non-asymptotic convergence rates of the approximation algorithm.
The paper analyzes the mean field Langevin dynamics and its convergence rate.
problem The convergence property of the mean field Langevin dynamics in the context of neural networks.
method The analysis uses a proximal Gibbs distribution and techniques from convex optimization.
result A concise convergence rate analysis of the mean field Langevin dynamics in both continuous and discrete time settings.
ICSGLD improves efficiency in posterior sampling for big data.
problem Efficient posterior sampling for large datasets.
method Embarrassingly parallel multiple-chain CSGLD with efficient interactions.
result ICSGLD is more efficient than a single-chain CSGLD.
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.
Study of Langevin dynamics for tensor PCA recovery in high dimensions.
problem Recovering hidden signal vectors (spikes) from noisy Gaussian tensor observations.
method Langevin dynamics approach for nonconvex optimization.
result Sample complexity matches the single-spike case but degrades for all spikes.
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.
Proposes a new method for constrained generative modeling using Langevin dynamics.
problem Challenges in satisfying underlying constraints with score-based generative models.
method Uses kinetic Langevin dynamics with specular reflection to model constraints.
result Demonstrates efficient numerical samplers with optimal convergence rates.
Alternative sampling method for autoregressive models using Langevin dynamics.
problem Efficiently sampling from autoregressive models.
method Initialize sequences with white noise and follow Langevin dynamics on global log-likelihood.
result Parallelizes and generalizes sampling process for autoregressive models.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
problem Recovering a planted signal in spiked matrix models.
method Path-wise characterization of overlap using integro-differential equations and explicit formula derivation.
result Sharp phase transition in limiting overlap: positive in one regime, zero in another due to injected noise.
A new algorithm improves Bayesian federated learning by reducing communication overhead.
problem Bayesian federated learning constraints, including privacy, data ownership, and communication overhead.
method Proposes Quantised Langevin Stochastic Dynamics (QLSD) for Bayesian federated learning, using gradient compression and variance reduction techniques.
result Non-asymptotic and asymptotic convergence guarantees for QLSD and its improved versions.
The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using Φ-divergence.
problem Analyzing convergence rates of Langevin dynamics and Proximal Sampler.
method Extending mixing time analyses to Φ-divergence, using strong data processing inequalities. result Convergence of Φ-divergence to 0 exponentially fast along Unadjusted Langevin Algorithm and Proximal Sampler. New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
Rapid mixing of Langevin dynamics on Riemannian manifolds
problem Mixing time of Langevin dynamics on Riemannian manifolds
method Relation between Langevin processes in domain and image
result Achievable polynomial mixing times
Efficiently simulates Langevin dynamics on manifold using diffusion maps and finite volume schemes.
problem Simulating Langevin dynamics on high-dimensional manifolds with limited data.
method Diffusion maps, Fokker-Planck equation, finite volume scheme, explicit time discretization.
result Data-driven finite volume scheme approximates Langevin dynamics on manifold with good properties.
Unified approach for sampling non-differentiable and heavy-tailed targets.
problem Sampling non-differentiable and heavy-tailed distributions using Langevin algorithms.
method Anchored Langevin dynamics, which modifies the Langevin diffusion with a smooth reference potential and multiplicative scaling.
result Non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution.
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
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.
New method uses higher-order Langevin dynamics for efficient parallel sampling.
problem Efficient parallel sampling from high-dimensional log-concave distributions.
method Combines higher-order Langevin dynamics with blockwise Lagrange polynomial interpolation.
result Reduces the number of parallel points required for a target accuracy.
The paper analyzes the InfoNCE loss under different temperature schedules using Langevin dynamics.
problem Understanding the dynamics of InfoNCE loss under fixed versus annealed temperature schedules.
method Modeling embedding evolution under Langevin dynamics on a compact Riemannian manifold, with theoretical guarantees for convergence.
result Slow logarithmic inverse-temperature schedules ensure convergence to globally optimal representations, while faster schedules risk suboptimal minima.
Paper proposes Langevin dynamics for adaptive IRL of stochastic gradient algorithms.
problem Estimating reward functions from noisy gradient estimates of stochastic gradient agents.
method Generalized Langevin dynamics algorithm for IRL.
result Proposed algorithms asymptotically generate samples proportional to exp(R(θ)).
Langevin Dynamics fails to sample from mixture distributions efficiently.
problem Analyzing Langevin Dynamics for sampling from mixture distributions.
method Theoretical analysis of Langevin Dynamics and proposing Chained-Langevin Dynamics.
result Langevin Dynamics fails to sample from mixture distributions efficiently.
Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.
problem Sampling from noisy posterior distributions efficiently.
method Annealed Langevin dynamics combined with diffusion models.
result Achieves posterior sampling in polynomial time with a weaker score error bound.
Improved error estimate for SGLD sampling algorithm.
problem Establishing a precise error bound for SGLD.
method Sharp uniform-in-time error estimate for SGLD under mild assumptions.
result Uniform-in-time O(η2) bound for KL-divergence between SGLD and Langevin diffusion. New method optimizes non-linear functionals over probability measures.
problem Optimizing non-linear functionals defined over probability measures.
method N-particle underdamped Langevin algorithm with spacetime discretization.
result Converges globally in total variation distance.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
Model infers latent variables in sparse coding models using Langevin dynamics.
problem Sampling posterior distribution in sparse coding models.
method Langevin dynamics for inference and simultaneous learning of parameters.
result Langevin dynamics efficiently sample from 'L0 sparse' posterior distribution.
Poisson Midpoint Method improves Langevin Dynamics for diffusion models.
problem Slow convergence of LMC in diffusion models requiring many small steps.
method Poisson Midpoint Method approximates LMC with larger steps, proving quadratic speed up.
result Poisson Midpoint Method maintains quality of DDPM with fewer calls.
Develops unbiased estimation method using underdamped Langevin dynamics.
problem Estimating expectations of non-negative Lebesgue density probability measures.
method Underdamped Langevin dynamics, time-discretized versions, doubly randomized estimation.
result Proves finite variance and expected/finite cost of the proposed estimator.
Geometric tempering fails for Langevin dynamics, proving convergence limits.
problem Proving convergence and limitations of geometric tempering for Langevin dynamics.
method Theoretical investigation of geometric tempering using Langevin dynamics.
result Geometric tempering can lead to exponential time convergence and poor functional inequalities.