In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometr…
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48 results for “Langevin process”
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.
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.
Uncertainty quantification of neural network models of evolving processes via Langevin samplingcs.LG
A scalable framework uses Langevin sampling to approximate neural network models of evolving processes.
problem Uncertainty quantification in neural network models of dynamic systems.
method Flexible data model based on NODE, joint learning of data model and posterior parameters, Langevin sampling.
result Demonstrated performance on chemical reaction and material physics data, compared favorably to variational inference.
Learning non-stationary Langevin dynamics from stochastic observations of latent trajectoriesstat.ML
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.
New process explains asset volatility patterns.
problem Explains statistical relationship between asset volatility and returns.
method Uses multiplicative Langevin process with adjustable coherence time.
result Exactly equivalent to Inverse Gamma distribution for volatility.
The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using -divergence.
problem Analyzing convergence rates of Langevin dynamics and Proximal Sampler.
method Extending mixing time analyses to -divergence, using strong data processing inequalities.
result Convergence of -divergence to 0 exponentially fast along Unadjusted Langevin Algorithm and Proximal Sampler.
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
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.
The paper analyzes sampling and estimation on manifolds using Langevin diffusion.
problem Sampling and estimation on compact Riemannian manifolds.
method Discretization of Langevin diffusion with error bounds derived.
result First-order error bounds for bias and variance in estimators.
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
Defending Diffusion Models Against Membership Inference Attacks via Higher-Order Langevin Dynamicscs.LG
Paper defends diffusion models from membership inference attacks using Langevin dynamics.
problem Defending diffusion models against membership inference attacks.
method Uses critically-damped higher-order Langevin dynamics with auxiliary variables.
result Demonstrates improved resistance to membership inference attacks through theoretical investigation and validation.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and state-dependent and the potential function can be non-convex. We show that the key p…
KIPLMC methods improve statistical inference in latent variable models.
problem Statistical inference in latent variable models.
method Joint diffusion process in parameter and latent variable spaces, with two explicit discretizations.
result KIPLMC methods achieve accelerated convergence rates in Wasserstein-2 distance.
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.
Langevin Dynamics for Adaptive Inverse Reinforcement Learning of Stochastic Gradient Algorithmscs.LG
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)).
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.
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.
Proposes a new Langevin flow approach for VAEs.
problem Difficulty in constructing low variance ELBO for VAEs with large datasets.
method Integrates Langevin dynamic with quasi-symplectic integrator to improve posterior estimation.
result Shows theoretical and practical effectiveness compared to gradient flow-based methods.
New simulation method tackles sign problem in quantum fields.
problem Sign problem in real-time dynamics of quantum fields.
method Inspired by reinforcement learning, complex Langevin approach with learned optimal kernels.
result Significant extension of real-time simulations in 1+1d scalar field theory.
Stabilizing Training of Generative Adversarial Nets via Langevin Stein Variational Gradient Descentcs.LG
Paper proposes LSVGD to stabilize GAN training via Langevin Stein Variational Gradient Descent.
problem Mode collapse and performance deterioration in GAN training.
method Langevin Stein Variational Gradient Descent (LSVGD) incorporating noise to stabilize training.
result LSVGD improves performance and stability of various GAN models.
Novel method for nonlinear data assimilation using Langevin sampling.
problem Nonlinear data assimilation challenges in Bayesian filtering.
method Score-based sequential Langevin sampling (SSLS) with dynamic models and annealing.
result Asymptotic stability and error bounds for local posterior sampling.
Improved generative models using critically-damped Langevin diffusion.
problem Current score-based generative models (SGMs) use overly simplistic diffusion processes, leading to complex denoising tasks and suboptimal performance.
method Proposed a novel critically-damped Langevin diffusion (CLD) and derived a score matching objective and sampling scheme.
result CLD-based SGMs achieve superior performance in synthesis quality compared to previous methods.
Pavlov Learning Machinescond-mat.dis-nn
Paper models Pavlov's classical conditioning using stochastic processes and Langevin equations.
problem Lack of modeling for Pavlov's classical conditioning.
method Modeling neural and synaptic dynamics via Langevin equations.
result Pavlov's mechanism spontaneously leads to synaptic weights similar to Hebb's.
New transport method simplifies cutoff phenomenon for Markov processes.
problem Understanding the cutoff phenomenon for Markov processes.
method A new W-TV transport inequality combined with a parabolic regularization estimate.
result Recovery and extension of previous results on cutoff phenomena.
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
Generative model uses Schrödinger bridges for stable sampling.
problem Sampling from unknown distributions with limited training samples.
method Combines Schrödinger bridges and Langevin dynamics.
result Effective stability and generation of samples within convex hull.
A standard form of master equations for general non-Markovian jump processes: the Laplace-space embedding framework and asymptotic solutioncond-mat.stat-mech
Unified analytical tool for non-Markovian jump processes.
problem Analyzing history-dependent jump processes with non-Markovian behavior.
method Developed a standard form of master equations using Laplace-space embedding and asymptotic solution.
result Unified analytical toolset for general non-Markovian processes, leading to the GLE approximation.
New method uses birth-death process and exploration component to accelerate sampling from multimodal distributions.
problem Sampling from multimodal probability distributions efficiently.
method Combines birth-death process and exploration component to accelerate sampling.
result Proves exponential asymptotic convergence under mild assumptions.
Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Modelsstat.ME
New method for Bayesian inference on large datasets.
problem Scalable sampling for Bayesian generalized linear mixed models on large datasets.
method Mirror Langevin dynamics with data subsampling, post-processing for variance estimation.
result Asymptotic, order-wise correct estimation of posterior variance.
Langevin algorithms improve training of very deep neural networks, especially for image classification.
problem Training very deep neural networks is challenging due to increased non-linearity and the risk of getting stuck in local minima.
method Comparison of Langevin and non-Langevin algorithms for training deep neural networks, introduction of Layer Langevin algorithm.
result Langevin algorithms, especially Layer Langevin, lead to significant improvements in training deep neural networks, particularly for image classification tasks.
New algorithm learns LQR with regret using Langevin dynamics and excitation.
problem Learning LQR with a regret bound.
method Thompson sampling with Langevin dynamics and excitation mechanism.
result Achieved regret bound for LQR learning.
Efficiently samples posterior distributions using Langevin dynamics.
problem Challenges in generating diverse posterior samples in high-dimensional spaces.
method Simulates Langevin dynamics in the noise space of a pre-trained generative model.
result Noise-space Langevin dynamics approximates the posterior without restarting the full sampling chain.
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.
New analysis shows temperature guarantees generalization in stochastic training.
problem Analyzing the generalization gap in stochastic training algorithms.
method Analyzing Langevin dynamics with positive temperature and bounding the generalization gap.
result Bounding the generalization gap by √(βE[L(θ_0)] + log(1/δ))/√N with probability 1-δ.
SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
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 approximates sampling from smooth potential distributions using a vanishing penalty.
problem Sampling from smooth potential distributions on high-dimensional spaces.
method Penalized Langevin dynamics (PLD) with vanishing penalty.
result Established upper bound on Wasserstein-2 distance for PLD approximation.
Method learns radial basis function distributions from samples.
problem Learning radial basis function distributions from training samples.
method Projected particle Langevin optimization method with distributionally robust optimization.
result Empirical measure of Langevin particles converges to a reflected Itô diffusion-drift process.
CSGM framework applied to clinical MRI data for robust reconstructions.
problem Applying deep generative priors to clinical MRI data for high-quality reconstructions.
method Training a generative prior on brain scans from the fastMRI dataset and using Langevin dynamics for posterior sampling.
result Posterior sampling via Langevin dynamics achieves high quality reconstructions in clinical MRI data.
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order . Our result holds as long as the continuous diffusion process associated with the algorithm converges exponentially fa…
A new TS-SA method alleviates non-stationarity in TS algorithms for bandits.
problem Non-stationarity in existing TS algorithms for multi-armed bandits.
method Integrates stochastic approximation within TS framework, using Langevin Monte Carlo and SA steps.
result Establishes near-optimal regret bounds for TS-SA, with simplified analysis.
Study adaptive sensing of Cox processes using posterior sampling and positive bases.
problem Adaptive sensing of Cox point processes with intensity function modeling.
method Model intensity function as truncated Gaussian process in positive basis, use Langevin dynamics and posterior sampling.
result Demonstrated improved sensing compared to classical Bayesian experimental design.
A new framework RTK accelerates diffusion inference by breaking down the process into fewer, more efficient subproblems.
problem Efficiently generating data from trained diffusion models using discretized reverse SDEs or ODEs.
method Developed a general RTK framework that decomposes the diffusion process into fewer, more balanced subproblems, using MALA and ULD for sampling.
result The RTK-MALA and RTK-ULD algorithms achieve faster convergence rates and lower error compared to existing methods.
Langevin processes, agent models and socio-economic systemscond-mat.stat-mech
We review some approaches to the understanding of fluctuations in some models used to describe socio and economic systems. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of th…
Accelerates convergence in global non-convex optimization with reversible diffusion.
problem Global non-convex optimization challenges.
method Utilizes reversible diffusion processes with adaptive diffusion coefficients.
result Accelerated convergence with reduced discretization error.
New method improves sampling from score-based models by correcting bias.
problem Bias in sampling from score-based diffusion models.
method Metropolis-Hastings or Barker's accept-reject steps to correct bias, using the score function.
result Improves sample quality on synthetic and image datasets, yielding consistent gains in FID.