Identifying the Group-Theoretic Structure of Machine-Learned Symmetries Article Swipe

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Roy T. Forestano , K. Matchev , Katia Matcheva , Alexander Roman , Eyup B. Unlu , Sarunas Verner ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2309.07860

Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later stage. In this letter we propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. We design loss functions which probe the subalgebra structure either during the deep learning stage of symmetry discovery or in a subsequent post-processing stage. We illustrate the new methods with examples from the U(n) Lie group family, obtaining the respective subalgebra decompositions. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries like SU(3) and SU(5) which are commonly used in model building.

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Abelian Group

Computer Science

Theoretical Physics

Artificial Intelligence

Physics

Theoretical Computer Science

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Homogeneous space Subalgebra Abelian group Group (periodic table) Symmetry (geometry) Lie group Symmetry group Identification (biology) Computer science Pure mathematics Theoretical physics Spacetime symmetries Artificial intelligence Algebra over a field Physics Theoretical computer science Mathematics Quantum mechanics Geometry Quantum Quantum field theory in curved spacetime Biology Quantum gravity Botany

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2309.07860
PDF: https://arxiv.org/pdf/2309.07860
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DOI: https://doi.org/10.48550/arxiv.2309.07860

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Title: Identifying the Group-Theoretic Structure of Machine-Learned Symmetries

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Language: en

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Publication year: 2023

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Publication date: 2023-09-14

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Authors: Roy T. Forestano, K. Matchev, Katia Matcheva, Alexander Roman, Eyup B. Unlu, Sarunas Verner

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Concepts: Homogeneous space, Subalgebra, Abelian group, Group (periodic table), Symmetry (geometry), Lie group, Symmetry group, Identification (biology), Computer science, Pure mathematics, Theoretical physics, Spacetime symmetries, Artificial intelligence, Algebra over a field, Physics, Theoretical computer science, Mathematics, Quantum mechanics, Geometry, Quantum, Quantum field theory in curved spacetime, Biology, Quantum gravity, Botany

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abstract_inverted_index.illustrate	73
abstract_inverted_index.respective	87
abstract_inverted_index.subalgebra	55, 88
abstract_inverted_index.subsequent	69
abstract_inverted_index.symmetries	26, 103, 111
abstract_inverted_index.techniques	19
abstract_inverted_index.application	92
abstract_inverted_index.demonstrate	97
abstract_inverted_index.identifying	40
abstract_inverted_index.non-Abelian	109
abstract_inverted_index.quantities.	14
abstract_inverted_index.spontaneous	106
abstract_inverted_index.symmetries.	47
abstract_inverted_index.successfully	4
abstract_inverted_index.identification	22, 99
abstract_inverted_index.decompositions.	89
abstract_inverted_index.group-theoretic	42
abstract_inverted_index.machine-learned	46
abstract_inverted_index.post-processing	70
abstract_inverted_index.transformations	9
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
citation_normalized_percentile