mlsanityData to 7 Oct 2026

Machine learning a manifold

arXiv 2112.07673 ↗First posted 14 Dec 2021hep-ph cs.LGcited by 9

Not on the map. Why?

Abstract (arXiv)

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 O(ε2) 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 minimised. We demonstrate our method in the SU(3)-symmetric (non-) linear Sigma model.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 3 of its 19 references that are in the map. First posted on arXiv 14 Dec 2021.

Builds on

3 of 19 references.

References · 3

  1. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  2. 2020Learning Invariances in Neural Networkscited by 52
  3. 2020Machine Learning Lie Structures & Applications to Physicscited by 13

Built on by

Cited by year

Citing papers per year: 2023: 5; 2024: 2; 2025: 2.

9 papers.

  1. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  2. 2024Symmetry Discovery Beyond Affine Transformationscited by 14
  3. 2023Discovering Sparse Representations of Lie Groups with Machine Learningcited by 8
  4. 2023Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6cited by 6
  5. 2023Identifying the Group-Theoretic Structure of Machine-Learned Symmetriescited by 6
  6. 2023Oracle-Preserving Latent Flowscited by 5
  7. 2024SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservationcited by 1
  8. 2025Unraveling particle dark matter with Physics-Informed Neural Networkscited by 1
  9. 2025Non-Gaussianities in Collider Metric Binningcited by 0