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Learning a local symmetry with neural networks

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Publication Date
2019-11-06
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Decelle, A.
Seoane, B.
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American Physical Society
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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.
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©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).
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