Decelle, Aurelien FabriceMartín Mayor, VíctorSeoane Bartolomé, Beatriz2023-06-162023-06-162019-11-062470-004510.1103/PhysRevE.100.050102https://hdl.handle.net/20.500.14352/5980©2019 American Physical Society. We thank L. A. Fernandez for encouraging discussions and Marco Baity-Jesi for his careful reading of the manuscript. This work was partially supported by Ministerio de Economia, Industria y Competitividad (MINECO) (Spain) and by EU's FEDER program through Grants No. FIS2015-65078-C2-1-P and No. PGC2018-094684-B-C21 and by the LabEx CALSIMLAB (public Grant No. ANR-11-LABX-0037-01 constituting a part of the "Investissements d'Avenir" program - reference No. ANR-11-IDEX-0004-02).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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevE.100.050102https://journals.aps.orgopen access53RelaxationFísica (Física)22 Física