Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the a...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2023-01-01
|
| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acd989 |
| _version_ | 1797808864623591424 |
|---|---|
| author | Roy T Forestano Konstantin T Matchev Katia Matcheva Alexander Roman Eyup B Unlu Sarunas Verner |
| author_facet | Roy T Forestano Konstantin T Matchev Katia Matcheva Alexander Roman Eyup B Unlu Sarunas Verner |
| author_sort | Roy T Forestano |
| collection | DOAJ |
| description | We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group $SO(1,3)$ . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties. |
| first_indexed | 2024-03-13T06:44:00Z |
| format | Article |
| id | doaj.art-2098782f296742879fa7c447dac4f841 |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-03-13T06:44:00Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-2098782f296742879fa7c447dac4f8412023-06-08T08:02:58ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014202502710.1088/2632-2153/acd989Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principlesRoy T Forestano0https://orcid.org/0000-0002-0355-2076Konstantin T Matchev1https://orcid.org/0000-0003-4182-9096Katia Matcheva2https://orcid.org/0000-0003-3074-998XAlexander Roman3https://orcid.org/0000-0003-2719-221XEyup B Unlu4https://orcid.org/0000-0002-6683-6463Sarunas Verner5https://orcid.org/0000-0003-4870-0826Institute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaInstitute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaInstitute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaInstitute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaInstitute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaInstitute for Fundamental Theory, Physics Department, University of Florida , Gainesville, FL 32611, United States of AmericaWe design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group $SO(1,3)$ . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.https://doi.org/10.1088/2632-2153/acd989symmetriessubalgebrasmachine-learningLorentz groupLie algebrassupervised learning |
| spellingShingle | Roy T Forestano Konstantin T Matchev Katia Matcheva Alexander Roman Eyup B Unlu Sarunas Verner Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles Machine Learning: Science and Technology symmetries subalgebras machine-learning Lorentz group Lie algebras supervised learning |
| title | Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles |
| title_full | Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles |
| title_fullStr | Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles |
| title_full_unstemmed | Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles |
| title_short | Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles |
| title_sort | deep learning symmetries and their lie groups algebras and subalgebras from first principles |
| topic | symmetries subalgebras machine-learning Lorentz group Lie algebras supervised learning |
| url | https://doi.org/10.1088/2632-2153/acd989 |
| work_keys_str_mv | AT roytforestano deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples AT konstantintmatchev deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples AT katiamatcheva deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples AT alexanderroman deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples AT eyupbunlu deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples AT sarunasverner deeplearningsymmetriesandtheirliegroupsalgebrasandsubalgebrasfromfirstprinciples |