Thinned Mean Field Langevin Dynamics

• URL: http://arxiv.org/abs/2605.28589v1
• Date: Wed, 27 May 2026 15:10:34 GMT
• Title: Thinned Mean Field Langevin Dynamics
• Abstract summary: Mean-field Langevin dynamics (MFLD) facilitate computation in this general context.<n>We propose textttKT-MFLD, in which each particle interacts only with a thinned particle coreset of size $mathcalO(Nfrac12)$.
• Score: 25.786764617149235
• License: http://creativecommons.org/licenses/by/4.0/
• 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 of order $N^2$. Motivated by recent research into \emph{kernel thinning}, we propose \texttt{KT-MFLD}, in which each particle interacts only with a thinned particle coreset of size $\mathcal{O}(N^{\frac{1}{2}})$. \texttt{KT-MFLD} thus reduces the computational complexity to order $N^{\frac{3}{2}}$ 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.

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