# Thinned Mean Field Langevin Dynamics

arXiv: https://arxiv.org/abs/2605.28589 · HTML: https://mlsanity.com/paper/2605.28589/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 84 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 30 of 40)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach](https://mlsanity.com/paper/1805.00915/) (2018)
- [Mean-Field Langevin Dynamics: Exponential Convergence and Annealing](https://mlsanity.com/paper/2202.01009/) (2022)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Convex Analysis of the Mean Field Langevin Dynamics](https://mlsanity.com/paper/2201.10469/) (2022)
- [Stochastic Particle Gradient Descent for Infinite Ensembles](https://mlsanity.com/paper/1712.05438/) (2017)
- [Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks](https://mlsanity.com/paper/1905.07769/) (2019)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [Emergence and scaling laws in SGD learning of shallow neural networks](https://mlsanity.com/paper/2504.19983/) (2025)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Generalized Kernel Thinning](https://mlsanity.com/paper/2110.01593/) (2021)
- [Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction](https://mlsanity.com/paper/2306.07221/) (2023)
- [Distribution Compression in Near-linear Time](https://mlsanity.com/paper/2111.07941/) (2021)
- [(De)-regularized Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/2409.14980/) (2024)
- [Optimal quantisation of probability measures using maximum mean discrepancy](https://mlsanity.com/paper/2010.07064/) (2020)
- [Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior](https://mlsanity.com/paper/2406.07475/) (2024)
- [Improved Particle Approximation Error for Mean Field Neural Networks](https://mlsanity.com/paper/2405.15767/) (2024)
- [The Alternating Descent Conditional Gradient Method for Sparse Inverse Problems](https://mlsanity.com/paper/1507.01562/) (2015)
- [Debiased Distribution Compression](https://mlsanity.com/paper/2404.12290/) (2024)
- [Prediction-Centric Uncertainty Quantification via MMD](https://mlsanity.com/paper/2410.11637/) (2024)
- [Low-Rank Thinning](https://mlsanity.com/paper/2502.12063/) (2025)
- [Interacting Particle Markov Chain Monte Carlo](https://mlsanity.com/paper/1602.05128/) (2016)

## Built on by (most cited first, 1 of 1)

- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)

## Abstract (arXiv)

Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context, casting the minimizer as the invariant distribution of a McKean--Vlasov process, which can be numerically discretized using N particles and thus simulated. However, simulating this interacting particle system has computational complexity of order N2. Motivated by recent research into kernel thinning, we propose textttKT-MFLD, in which each particle interacts only with a thinned particle coreset of size O(N^frac12). textttKT-MFLD thus reduces the computational complexity to order N^frac32 while, under mild regularity conditions, achieving the same convergence guarantees (up to logarithmic factors) as MFLD. Our theoretical analysis is empirically confirmed on tasks including the training of student-teacher neural networks, quantization with maximum mean discrepancy, and computation of predictively-oriented posteriors in a post-Bayesian framework.