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  • Open Access

Machine-Learned Renormalization-Group-Improved Gauge Actions and Classically Perfect Gradient Flows

Kieran Holland1,*, Andreas Ipp2,†, David I. Müller2,‡, and Urs Wenger3,§

  • 1University of the Pacific, 3601 Pacific Avenue, Stockton, California 95211, USA
  • 2Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
  • 3Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstraße 5, CH-3012 Bern, Switzerland

  • *Contact author: kholland@pacific.edu
  • †Contact author: ipp@hep.itp.tuwien.ac.at
  • ‡Contact author: dmueller@hep.itp.tuwien.ac.at
  • §Contact author: wenger@itp.unibe.ch
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Phys. Rev. Lett. 136, 031901 – Published 21 January, 2026

DOI: https://doi.org/10.1103/k41k-2pnc

Abstract

Extracting continuum properties of quantum field theories from discretized spacetime is challenging due to lattice artifacts. Renormalization-group (RG)-improved lattice actions can preserve continuum properties, but are in general difficult to parameterize. Machine learning (ML) with gauge-equivariant convolutional neural networks provides a way to efficiently describe such actions. We test a machine-learned RG-improved lattice gauge action, the classically perfect fixed-point (FP) action, for four-dimensional SU(3) gauge theory through Monte Carlo simulations. We establish that the gradient flow of the FP action is free of tree-level discretization effects to all orders in the lattice spacing, making it classically perfect. This allows us to test the quality of improvement of the FP action, without introducing additional artifacts. We find that discretization effects in gradient-flow observables are highly suppressed and less than 1% up to lattice spacings of 0.14 fm, allowing continuum physics to be extracted from coarse lattices. The quality of improvement achieved motivates the use of the FP action in future gauge theory studies. The advantages of ML-based parameterizations also highlight the possibility of realizing quantum perfect actions in lattice gauge theory.

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Phys. Rev. Lett. 136, 031901– Published 21 January, 2026
  • Received 12 May 2025
  • Accepted 18 December 2025
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