# Non-reversible Parallel Tempering for Deep Posterior Approximation

arXiv: https://arxiv.org/abs/2211.10837 · HTML: https://mlsanity.com/paper/2211.10837/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 20 Nov 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [Benign Overfitting of Constant-Stepsize SGD for Linear Regression](https://mlsanity.com/paper/2103.12692/) (2021)
- [A statistical theory of cold posteriors in deep neural networks](https://mlsanity.com/paper/2008.05912/) (2020)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Tight Nonparametric Convergence Rates for Stochastic Gradient Descent under the Noiseless Linear Model](https://mlsanity.com/paper/2006.08212/) (2020)
- [Non-convex Learning via Replica Exchange Stochastic Gradient MCMC](https://mlsanity.com/paper/2008.05367/) (2020)
- [Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget](https://mlsanity.com/paper/1304.5299/) (2013)
- [Speeding Up MCMC by Efficient Data Subsampling](https://mlsanity.com/paper/1404.4178/) (2014)
- [Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion](https://mlsanity.com/paper/2007.01990/) (2020)
- [An Efficient Minibatch Acceptance Test for Metropolis-Hastings](https://mlsanity.com/paper/1610.06848/) (2016)
- [Replica Exchange for Non-Convex Optimization](https://mlsanity.com/paper/2001.08356/) (2020)
- [Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction](https://mlsanity.com/paper/2010.01084/) (2020)
- [Interacting Contour Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2202.09867/) (2022)

## Built on by (most cited first, 7 of 7)

- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2405.07839/) (2024)
- [Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs](https://mlsanity.com/paper/2502.00550/) (2025)
- [Enhancing Gradient-based Discrete Sampling via Parallel Tempering](https://mlsanity.com/paper/2502.19240/) (2025)
- [Position: The Time for Sampling Is Now! Charting a New Course for Bayesian Deep Learning](https://mlsanity.com/paper/2605.21765/) (2026)
- [Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation](https://mlsanity.com/paper/2604.05303/) (2026)
- [Explore Broadly, Reason Sharply: Push Small Models toward the Frontier via Sampling](https://mlsanity.com/paper/2609.38104/) (2026)

## Abstract (arXiv)

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from O(P2) to O(P) given sufficiently many P chains. However, such an innovation largely disappears in big data due to the limited chains and few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote non-reversibility and propose a few solutions to tackle the underlying bias caused by the geometric stopping time. Notably, in big data scenarios, we obtain an appealing communication cost O(Plog P) based on the optimal window size. In addition, we also adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct approximation tasks for complex posteriors without much tuning costs.