# Stochastic Gradient MCMC with Repulsive Forces

arXiv: https://arxiv.org/abs/1812.00071 · HTML: https://mlsanity.com/paper/1812.00071/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2018.

## Built on by (most cited first, 18 of 18)

- [On Stein Variational Neural Network Ensembles](https://mlsanity.com/paper/2106.10760/) (2021)
- [Neural Variational Gradient Descent](https://mlsanity.com/paper/2107.10731/) (2021)
- [Stein Variational Gradient Descent: many-particle and long-time asymptotics](https://mlsanity.com/paper/2102.12956/) (2021)
- [Personalizing Text-to-Image Generation via Aesthetic Gradients](https://mlsanity.com/paper/2209.12330/) (2022)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [Feature Space Particle Inference for Neural Network Ensembles](https://mlsanity.com/paper/2206.00944/) (2022)
- [Annealed Stein Variational Gradient Descent for Improved Uncertainty Estimation in Full-Waveform Inversion](https://mlsanity.com/paper/2410.13249/) (2024)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)
- [De-randomizing MCMC dynamics with the diffusion Stein operator](https://mlsanity.com/paper/2110.03768/) (2021)
- [Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow](https://mlsanity.com/paper/2605.09456/) (2026)
- [Parameter Expanded Stochastic Gradient Markov Chain Monte Carlo](https://mlsanity.com/paper/2503.00699/) (2025)
- [ELBOing Stein: Variational Bayes with Stein Mixture Inference](https://mlsanity.com/paper/2410.22948/) (2024)
- [JaxSGMC: Modular stochastic gradient MCMC in JAX](https://mlsanity.com/paper/2505.11190/) (2025)
- [Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversion](https://mlsanity.com/paper/2212.14595/) (2022)
- [Stein Variational Newton Neural Network Ensembles](https://mlsanity.com/paper/2411.01887/) (2024)
- [Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks](https://mlsanity.com/paper/2605.07060/) (2026)
- [Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials](https://mlsanity.com/paper/2606.04100/) (2026)
- [Interacting particle guidance for sampling reward-tilted generative priors](https://mlsanity.com/paper/2609.37227/) (2026)

## Abstract (arXiv)

We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCMC method. Instead of treating each parallel chain independently from others, our proposed algorithm implements a repulsive force between particles, avoiding collapse and facilitating a better exploration of the parameter space. We also show how the addition of this noise term is necessary to obtain a valid SG-MCMC sampler, a significant difference with SVGD. Experiments with both synthetic distributions and real datasets illustrate the benefits of the proposed scheme.