# Efficient Learning of Lattice Gauge Theories with Fermions

arXiv: https://arxiv.org/abs/2512.19891 · HTML: https://mlsanity.com/paper/2512.19891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 3 of 3)

- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [Learning quantum Hamiltonians at any temperature in polynomial time](https://mlsanity.com/paper/2310.02243/) (2023)
- [Leveraging neural control variates for enhanced precision in lattice field theory](https://mlsanity.com/paper/2312.08228/) (2023)

## Abstract (arXiv)

We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.