# Deep learning lattice gauge theories

arXiv: https://arxiv.org/abs/2405.14830 · HTML: https://mlsanity.com/paper/2405.14830/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 2 of 2)

- [Applications of Lattice Gauge Equivariant Neural Networks](https://mlsanity.com/paper/2212.00832/) (2022)
- [Preserving gauge invariance in neural networks](https://mlsanity.com/paper/2112.11239/) (2021)

## Built on by (most cited first, 3 of 3)

- [Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories](https://mlsanity.com/paper/2604.20797/) (2026)
- [Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories](https://mlsanity.com/paper/2605.03901/) (2026)
- [Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2610.18742/) (2026)

## Abstract (arXiv)

Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of mathbbZN lattice gauge theories in 2+1 dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For mathbbZ2, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the mathbbZ3 case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.