# Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network

arXiv: https://arxiv.org/abs/2401.06481 · HTML: https://mlsanity.com/paper/2401.06481/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 60 references that are in the map.
- First posted on arXiv 12 Jan 2024.

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

- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://mlsanity.com/paper/2207.00283/) (2022)
- [Diffusion Models as Stochastic Quantization in Lattice Field Theory](https://mlsanity.com/paper/2309.17082/) (2023)
- [Normalizing flows for lattice gauge theory in arbitrary space-time dimension](https://mlsanity.com/paper/2305.02402/) (2023)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [Gauge-equivariant neural networks as preconditioners in lattice QCD](https://mlsanity.com/paper/2302.05419/) (2023)
- [Geometrical aspects of lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2303.11448/) (2023)
- [Gauge-equivariant pooling layers for preconditioners in lattice QCD](https://mlsanity.com/paper/2304.10438/) (2023)
- [Fixed point actions from convolutional neural networks](https://mlsanity.com/paper/2311.17816/) (2023)

## Built on by (most cited first, 2 of 2)

- [Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics](https://mlsanity.com/paper/2501.05580/) (2025)
- [Machine learning for four-dimensional SU(3) lattice gauge theories](https://mlsanity.com/paper/2604.12416/) (2026)

## Abstract (arXiv)

Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing one to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations and scaling studies.