# Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble

arXiv: https://arxiv.org/abs/2502.05784 · HTML: https://mlsanity.com/paper/2502.05784/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 30 of 37)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [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)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)
- [Model Ratatouille: Recycling Diverse Models for Out-of-Distribution Generalization](https://mlsanity.com/paper/2212.10445/) (2022)
- [AdapterSoup: Weight Averaging to Improve Generalization of Pretrained Language Models](https://mlsanity.com/paper/2302.07027/) (2023)
- [Mean-Field Langevin Dynamics: Exponential Convergence and Annealing](https://mlsanity.com/paper/2202.01009/) (2022)
- [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)
- [The Relative Performance of Ensemble Methods with Deep Convolutional Neural Networks for Image Classification](https://mlsanity.com/paper/1704.01664/) (2017)
- [Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks](https://mlsanity.com/paper/1905.07769/) (2019)
- [Uniform-in-time propagation of chaos for mean field Langevin dynamics](https://mlsanity.com/paper/2212.03050/) (2022)
- [Global convergence of neuron birth-death dynamics](https://mlsanity.com/paper/1902.01843/) (2019)

## Built on by (most cited first, 5 of 5)

- [Mirror Mean-Field Langevin Dynamics](https://mlsanity.com/paper/2505.02621/) (2025)
- [Weight-Decay Turns Transformer Loss Landscapes Villani: Functional-Analytic Foundations for Optimization and Generalization](https://mlsanity.com/paper/2605.06599/) (2026)
- [Thinned Mean Field Langevin Dynamics](https://mlsanity.com/paper/2605.28589/) (2026)
- [On propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization](https://mlsanity.com/paper/2602.15094/) (2026)
- [A Distributional Optimisation Perspective on Combining Models in Deep Learning](https://mlsanity.com/paper/2609.24328/) (2026)

## Abstract (arXiv)

Mean-field Langevin dynamics (MFLD) is an optimization method derived by taking the mean-field limit of noisy gradient descent for two-layer neural networks in the mean-field regime. Recently, the propagation of chaos (PoC) for MFLD has gained attention as it provides a quantitative characterization of the optimization complexity in terms of the number of particles and iterations. A remarkable progress by Chen et al. (2022) showed that the approximation error due to finite particles remains uniform in time and diminishes as the number of particles increases. In this paper, by refining the defective log-Sobolev inequality -- a key result from that earlier work -- under the neural network training setting, we establish an improved PoC result for MFLD, which removes the exponential dependence on the regularization coefficient from the particle approximation term of the optimization complexity. As an application, we propose a PoC-based model ensemble strategy with theoretical guarantees.