# Training neural control variates using correlated configurations

arXiv: https://arxiv.org/abs/2505.07719 · HTML: https://mlsanity.com/paper/2505.07719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Continuously Differentiable Exponential Linear Units](https://mlsanity.com/paper/1704.07483/) (2017)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [Neural Control Variates](https://mlsanity.com/paper/2006.01524/) (2020)
- [Vector-Valued Control Variates](https://mlsanity.com/paper/2109.08944/) (2021)
- [Regularized Zero-Variance Control Variates](https://mlsanity.com/paper/1811.05073/) (2018)
- [Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization](https://mlsanity.com/paper/2006.07487/) (2020)
- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [Theoretical guarantees for neural control variates in MCMC](https://mlsanity.com/paper/2304.01111/) (2023)
- [Leveraging neural control variates for enhanced precision in lattice field theory](https://mlsanity.com/paper/2312.08228/) (2023)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)

## Built on by (most cited first, 1 of 1)

- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)

## Abstract (arXiv)

Neural control variates (NCVs) have emerged as a powerful tool for variance reduction in Monte Carlo (MC) simulations, particularly in high-dimensional problems where traditional control variates are difficult to construct analytically. By training neural networks to learn auxiliary functions correlated with the target observable, NCVs can significantly reduce estimator variance while preserving unbiasedness. However, a critical but often overlooked aspect of NCV training is the role of autocorrelated samples generated by Markov Chain Monte Carlo (MCMC). While such samples are typically discarded for error estimation due to their statistical redundancy, they may contain useful information about the structure of the underlying probability distribution that can benefit the training process. In this work, we systematically examine the effect of using correlated configurations in training neural control variates. We demonstrate, both conceptually and numerically, that training on correlated data can improve control variate performance, especially in settings with limited computational resources. Our analysis includes empirical results from U(1) gauge theory and scalar field theory, illustrating when and how autocorrelated samples enhance NCV construction. These findings provide practical guidance for the efficient use of MCMC data in training neural networks.