Learning a local symmetry with neural networks



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Decelle, A. and Martín Mayor, Víctor and Seoane, B. (2019) Learning a local symmetry with neural networks. Physical review E, 100 (5). ISSN 2470-0045

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Official URL: http://dx.doi.org/10.1103/PhysRevE.100.050102


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.

Item Type:Article
Additional Information:

©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).

Uncontrolled Keywords:Relaxation
Subjects:Sciences > Physics
ID Code:58091
Deposited On:10 Jan 2020 16:47
Last Modified:13 Jan 2020 08:54

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