# Leveraging neural control variates for enhanced precision in lattice field theory

arXiv: https://arxiv.org/abs/2312.08228 · HTML: https://mlsanity.com/paper/2312.08228/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Builds on (most cited first, 1 of 1)

- [Neural Control Variates](https://mlsanity.com/paper/2006.01524/) (2020)

## Built on by (most cited first, 4 of 4)

- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)
- [Training neural control variates using correlated configurations](https://mlsanity.com/paper/2505.07719/) (2025)
- [Efficient Learning of Lattice Gauge Theories with Fermions](https://mlsanity.com/paper/2512.19891/) (2025)
- [Neural Autoregressive Control Variates for the Quantum Monte Carlo Sign Problem](https://mlsanity.com/paper/2605.26814/) (2026)

## Abstract (arXiv)

Results obtained with stochastic methods have an inherent uncertainty due to the finite number of samples that can be achieved in practice. In lattice QCD this problem is particularly salient in some observables like, for instance, observables involving one or more baryons and it is the main problem preventing the calculation of nuclear forces from first principles. The method of control variables has been used extensively in statistics and it amounts to computing the expectation value of the difference between the observable of interest and another observable whose average is known to be zero but is correlated with the observable of interest. Recently, control variates methods emerged as a promising solution in the context of lattice field theories. In our current study, instead of relying on an educated guess to determine the control variate, we utilize a neural network to parametrize this function. Using 1+1 dimensional scalar field theory as a testbed, we demonstrate that this neural network approach yields substantial improvements. Notably, our findings indicate that the neural network ansatz is particularly effective in the strong coupling regime.