Learning a Local Symmetry with Neural-Networks
This work addresses a domain-specific challenge in physics and computational complexity, but appears incremental as it builds on known methods for symmetry detection.
The authors tackled the problem of detecting the Z2 gauge symmetry, which is relevant for physical systems like spin-glasses and QCD, by designing a neural network and dataset to learn this symmetry and find compressed latent representations of gauge orbits, with a focus on system-wrapping loops (Polyakov loops) that affect computational complexity.
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.