Learning a local symmetry with neural networks

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 quantum chromodynamics, 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.