Thinned Mean Field Langevin Dynamics

Zonghao Chen, Heishiro Kanagawa, Francois-Xavier Briol, Chris J. Oates, Lester Mackey
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:14859-14883, 2026.

Abstract

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 $\mathcal{O}(N^2)$. Motivated by recent research into kernel thinning, we propose KT-MFLD, in which each particle interacts only with a coreset of size $\mathcal{O}(N^{\frac{1}{2}})$. KT-MFLD thus reduces the computational complexity to $\mathcal{O}(N^{\frac{3}{2}})$ 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26bd, title = {Thinned Mean Field {L}angevin Dynamics}, author = {Chen, Zonghao and Kanagawa, Heishiro and Briol, Francois-Xavier and Oates, Chris J. and Mackey, Lester}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {14859--14883}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26bd/chen26bd.pdf}, url = {https://proceedings.mlr.press/v306/chen26bd.html}, abstract = {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 $\mathcal{O}(N^2)$. Motivated by recent research into kernel thinning, we propose KT-MFLD, in which each particle interacts only with a coreset of size $\mathcal{O}(N^{\frac{1}{2}})$. KT-MFLD thus reduces the computational complexity to $\mathcal{O}(N^{\frac{3}{2}})$ 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.} }
Endnote
%0 Conference Paper %T Thinned Mean Field Langevin Dynamics %A Zonghao Chen %A Heishiro Kanagawa %A Francois-Xavier Briol %A Chris J. Oates %A Lester Mackey %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26bd %I PMLR %P 14859--14883 %U https://proceedings.mlr.press/v306/chen26bd.html %V 306 %X 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 $\mathcal{O}(N^2)$. Motivated by recent research into kernel thinning, we propose KT-MFLD, in which each particle interacts only with a coreset of size $\mathcal{O}(N^{\frac{1}{2}})$. KT-MFLD thus reduces the computational complexity to $\mathcal{O}(N^{\frac{3}{2}})$ 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.
APA
Chen, Z., Kanagawa, H., Briol, F., Oates, C.J. & Mackey, L.. (2026). Thinned Mean Field Langevin Dynamics. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:14859-14883 Available from https://proceedings.mlr.press/v306/chen26bd.html.

Related Material