# Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

arXiv: https://arxiv.org/abs/2111.10189 · HTML: https://mlsanity.com/paper/2111.10189/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 19 Nov 2021.

## Builds on (most cited first, 6 of 6)

- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)

## Built on by (most cited first, 10 of 10)

- [Hierarchical autoregressive neural networks for statistical systems](https://mlsanity.com/paper/2203.10989/) (2022)
- [Multilevel Generative Samplers for Investigating Critical Phenomena](https://mlsanity.com/paper/2503.08918/) (2025)
- [Simulating first-order phase transition with hierarchical autoregressive networks](https://mlsanity.com/paper/2212.04955/) (2022)
- [Mutual information of spin systems from autoregressive neural networks](https://mlsanity.com/paper/2304.13412/) (2023)
- [Gradient estimators for normalising flows](https://mlsanity.com/paper/2202.01314/) (2022)
- [Training normalizing flows with computationally intensive target probability distributions](https://mlsanity.com/paper/2308.13294/) (2023)
- [NeuMC -- a package for neural sampling for lattice field theories](https://mlsanity.com/paper/2503.11482/) (2025)
- [Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciences](https://mlsanity.com/paper/2511.07433/) (2025)
- [Variational Autoregressive Networks with probability priors](https://mlsanity.com/paper/2605.16020/) (2026)
- [Fixed-point neural samplers on discrete spaces](https://mlsanity.com/paper/2610.01739/) (2026)

## Abstract (arXiv)

We provide a deepened study of autocorrelations in Neural Markov Chain Monte Carlo (NMCMC) simulations, a version of the traditional Metropolis algorithm which employs neural networks to provide independent proposals. We illustrate our ideas using the two-dimensional Ising model. We discuss several estimates of autocorrelation times in the context of NMCMC, some inspired by analytical results derived for the Metropolized Independent Sampler (MIS). We check their reliability by estimating them on a small system where analytical results can also be obtained. Based on the analytical results for MIS we propose a new loss function and study its impact on the autocorelation times. Although, this function's performance is a bit inferior to the traditional Kullback-Leibler divergence, it offers two training algorithms which in some situations may be beneficial. By studying a small, 4 × 4, system we gain access to the dynamics of the training process which we visualize using several observables. Furthermore, we quantitatively investigate the impact of imposing global discrete symmetries of the system in the neural network training process on the autocorrelation times. Eventually, we propose a scheme which incorporates partial heat-bath updates which considerably improves the quality of the training. The impact of the above enhancements is discussed for a 16 × 16 spin system. The summary of our findings may serve as a guidance to the implementation of Neural Markov Chain Monte Carlo simulations for more complicated models.