mlsanityData to 14 Oct 2026

Discovering Sparse Representations of Lie Groups with Machine Learning

arXiv 2302.05383 ↗First posted 10 Feb 2023hep-ph cs.LG math-phcited by 8

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Abstract (arXiv)

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the U(n) and SU(n) families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 11 of its 18 references that are in the map. First posted on arXiv 10 Feb 2023.

Builds on

11 of 18 references.

References · 11

  1. 2018Discovering physical concepts with neural networkscited by 117
  2. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  3. 2020Detecting Symmetries with Neural Networkscited by 34
  4. 2020Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networkscited by 33
  5. 2021Machine-learning hidden symmetriescited by 31
  6. 2022LieGG: Studying Learned Lie Group Generatorscited by 31
  7. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  8. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
  9. 2021Symmetry meets AIcited by 13
  10. 2021Machine learning a manifoldcited by 9
  11. 2023Oracle-Preserving Latent Flowscited by 5

Built on by

Cited by year

Citing papers per year: 2023: 3; 2024: 3; 2025: 2.

8 papers.

  1. 2025Interpretable Machine Learning in Physics: A Reviewcited by 14
  2. 2023Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6cited by 6
  3. 2023Identifying the Group-Theoretic Structure of Machine-Learned Symmetriescited by 6
  4. 2023A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networkscited by 6
  5. 2024Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physicscited by 4
  6. 2024Quantum Rationale-Aware Graph Contrastive Learning for Jet Discriminationcited by 0
  7. 2024Lie-Equivariant Quantum Graph Neural Networkscited by 0
  8. 2025Non-Gaussianities in Collider Metric Binningcited by 0