PreprintCC BY 4.0arXiv
A variational framework for variance reduction in lattice field theory
Abstract
The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.
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BibTeX
@misc{butti2026variational,
title = {{A variational framework for variance reduction in lattice field theory}},
author = {Pietro Butti and Guilherme Catumba and Alessandro Nada and Louis Spatscheck},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28142},
eprint = {2609.28142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28142},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A variational framework for variance reduction in lattice field theory
AU - Pietro Butti
AU - Guilherme Catumba
AU - Alessandro Nada
AU - Louis Spatscheck
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28142
UR - https://arxiv.org/abs/2609.28142
AB - The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.
ER -