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Machine learning a manifold

Craven, Sean; Croon, Djuna; Cutting, Daniel; Houtz, Rachel

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Sean Craven

Daniel Cutting


We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the Oðϵ2Þ scaling of the output variable under infinitesimal symmetry transformations on the input variables. As symmetry transformations are generated post-training, the methodology does not rely on sampling of the full representation space or binning of the dataset, and the possibility of false identification is minimized. We demonstrate our method in the SU(3)-symmetric (non-) linear Σ model.


Craven, S., Croon, D., Cutting, D., & Houtz, R. (2022). Machine learning a manifold. Physical Review D, 105(9), Article 096030.

Journal Article Type Article
Acceptance Date May 4, 2022
Online Publication Date May 25, 2022
Publication Date 2022
Deposit Date Jul 26, 2022
Publicly Available Date Jul 26, 2022
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 105
Issue 9
Article Number 096030


Published Journal Article (341 Kb)

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Copyright Statement
Published by the American Physical Society under the terms of<br /> the Creative Commons Attribution 4.0 International license.<br /> Further distribution of this work must maintain attribution to<br /> the author(s) and the published article’s title, journal citation,<br /> and DOI. Funded by SCOAP3.

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