# On the mean field limit of consensus based methods

arXiv: https://arxiv.org/abs/2409.03518 · HTML: https://mlsanity.com/paper/2409.03518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [To discretize continually: Mean shift interacting particle systems for Bayesian inference](https://mlsanity.com/paper/2605.14142/) (2026)
- [Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization](https://mlsanity.com/paper/2511.21466/) (2025)

## Abstract (arXiv)

Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus based sampling (CBS). In this paper, we investigate the ``mean field limit'' of a class of consensus methods, including CBO and CBS. This limit allows to characterize the system's behavior as the number of particles approaches infinity. Building upon prior work such as (Huang and Qiu, 2022), we establish the existence of a unique, strong solution for these finite-particle SDEs. We further provide uniform moment estimates, which allow to show a Fokker-Planck equation in the mean-field limit. Finally, we prove that the limiting McKean-Vlasov type SDE related to the Fokker-Planck equation admits a unique solution.