Bias-Corrected Machine-Learning Estimation of Chiral Condensate Cumulants: A Retrospective Lattice QCD Case Study
Abstract
We present a retrospective case study of bias-corrected machine learning (ML) estimates of traces of the inverse Dirac operator, Tr M−n (n=1,2,3,4), using a fixed lattice QCD dataset and examining how the results depend on the relative proportions of the labeled and training sets. Two supervised learning approaches are examined: one using Tr M−1 as the input feature, and the other employing gauge observables such as the plaquette and rectangle. Beyond the direct estimation of Tr M−n, we further investigate two derived applications of the ML estimations: the evaluation of the cumulants of the chiral condensate within a single ensemble and that obtained through multi-ensemble reweighting across ensembles with different quark masses. Within this fixed dataset, the bias-corrected estimates show close agreement with the full-data reference under the adopted evaluation criteria, while the uncorrected estimates can exhibit amplified deviations after the nonlinear cumulant and reweighting steps. For the approach using Tr M−1 as the input feature, nominal solve-count accounting suggests that the Dirac-inversion cost could be reduced to approximately 25.75% of that of the conventional calculation in the present setup. This value is a cost projection rather than an end-to-end benchmark: it assumes comparable costs for successive inversions and excludes model-training and analysis overhead.
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BibTeX
@misc{choi2026biascorrected,
title = {{Bias-Corrected Machine-Learning Estimation of Chiral Condensate Cumulants: A Retrospective Lattice QCD Case Study}},
author = {Benjamin J. Choi and Hiroshi Ohno and Akio Tomiya},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30416},
eprint = {2608.30416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30416},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bias-Corrected Machine-Learning Estimation of Chiral Condensate Cumulants: A Retrospective Lattice QCD Case Study
AU - Benjamin J. Choi
AU - Hiroshi Ohno
AU - Akio Tomiya
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30416
UR - https://arxiv.org/abs/2608.30416
AB - We present a retrospective case study of bias-corrected machine learning (ML) estimates of traces of the inverse Dirac operator, Tr M^−n (n=1,2,3,4), using a fixed lattice QCD dataset and examining how the results depend on the relative proportions of the labeled and training sets. Two supervised learning approaches are examined: one using Tr M^−1 as the input feature, and the other employing gauge observables such as the plaquette and rectangle. Beyond the direct estimation of Tr M^−n, we further investigate two derived applications of the ML estimations: the evaluation of the cumulants of the chiral condensate within a single ensemble and that obtained through multi-ensemble reweighting across ensembles with different quark masses. Within this fixed dataset, the bias-corrected estimates show close agreement with the full-data reference under the adopted evaluation criteria, while the uncorrected estimates can exhibit amplified deviations after the nonlinear cumulant and reweighting steps. For the approach using Tr M^−1 as the input feature, nominal solve-count accounting suggests that the Dirac-inversion cost could be reduced to approximately 25.75% of that of the conventional calculation in the present setup. This value is a cost projection rather than an end-to-end benchmark: it assumes comparable costs for successive inversions and excludes model-training and analysis overhead.
ER -