Machine learning a manifold

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

Abstract

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.

Citation

Craven, S., Croon, D., Cutting, D., & Houtz, R. (2022). Machine learning a manifold. Physical Review D, 105(9), Article 096030. https://doi.org/10.1103/physrevd.105.096030

• 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
• DOI: https://doi.org/10.1103/physrevd.105.096030