Learning a Local Symmetry with Neural-Networks

Aurélien Decelle; Victor Martin-Mayor; Beatriz Seoane

doi:10.1103/physreve.100.050102

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arXiv · 1904.07637

Learning a Local Symmetry with Neural-Networks

Aurélien Decelle·Victor Martin-Mayor·Beatriz Seoane

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Abstract

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.

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cond-mat.dis-nn cond-mat.stat-mech cs.LG

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BibTeX RIS

Aurélien Decelle, Victor Martin-Mayor, Beatriz Seoane. 2019-04-16. Learning a Local Symmetry with Neural-Networks. https://doi.org/10.1103/physreve.100.050102

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