Learning a local symmetry with neural networks

Aurélien Decelle (1) , Victor Martin-Mayor , Beatriz Seoane (2)

1 LRI - Laboratoire de Recherche en Informatique
2 LCQB - Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns: the gauge symmetry Z2. 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.

Mots clés: Statistical Physics

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]

Aurélien Decelle, Victor Martin-Mayor, Beatriz Seoane. Learning a local symmetry with neural networks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2019, 100 (5), pp.050102. ⟨10.1103/PhysRevE.100.050102⟩. ⟨hal-02403561⟩