# Learning a Local Symmetry with Neural-Networks

## TL;DR

This paper demonstrates how neural networks can be designed to detect complex local symmetries, specifically Z2 gauge symmetry, and learn compressed representations relevant for physical and computational problems.

## Contribution

It introduces a neural network architecture and dataset tailored to learn Z2 gauge symmetry and captures key features like Polyakov loops affecting computational complexity.

## Key findings

- Neural networks can learn local gauge symmetries from data.
- The method captures key physical features such as Polyakov loops.
- The approach enables compressed latent representations of gauge orbits.

## Abstract

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns : the gauge symmetry Z 2 . This symmetry is present in physical problems from topological transitions to QCD, and controls the computational hardness of instances of spin-glasses. Here, we show how to design a neural network, and a dataset, able to learn this symmetry and to find compressed latent representations of the gauge orbits. Our method pays special attention to system-wrapping loops, the so-called Polyakov loops, known to be particularly relevant for computational complexity.