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Lorentz Group Equivariant Neural Network for Particle Physics

arXiv 2006.04780 ↗First posted 8 Jun 2020hep-ph cs.LG hep-excited by 120

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Abstract (arXiv)

We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use CNNs and point cloud approaches. The competitive performance of the network is demonstrated on a public classification dataset [27] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.

Key facts. Cited by 120 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jun 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 30; 2023: 24; 2024: 20; 2025: 15; 2026: 9.

120 papers.

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  1. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  2. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  3. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  4. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  5. 2022Particle Transformer for Jet Taggingcited by 95
  6. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  7. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  8. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  9. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 74
  10. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  11. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  12. 2023Clifford Group Equivariant Neural Networkscited by 54
38 more
  1. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  2. 2021Machine Learning in the Search for New Fundamental Physicscited by 50
  3. 2021Learning Partial Equivariances from Datacited by 44
  4. 2021Efficient Differentiable Simulation of Articulated Bodiescited by 38
  5. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  6. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  7. 2021Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atzecited by 29
  8. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 28
  9. 2022Interpretable Geometric Deep Learning via Learnable Randomness Injectioncited by 27
  10. 2022PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physicscited by 26
  11. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  12. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  13. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  14. 2023Explainable Equivariant Neural Networks for Particle Physics: PELICANcited by 22
  15. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  16. 2022What is an equivariant neural network?cited by 21
  17. 2024Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Modelscited by 21
  18. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 18
  19. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  20. 2022On the non-universality of deep learning: quantifying the cost of symmetrycited by 17
  21. 2022Brauer's Group Equivariant Neural Networkscited by 17
  22. 2021Equivariant Networks for Pixelized Spherescited by 16
  23. 2023A General Framework for Equivariant Neural Networks on Reductive Lie Groupscited by 16
  24. 2022Lorentz group equivariant autoencoderscited by 15
  25. 2021A FAIR and AI-ready Higgs boson decay datasetcited by 14
  26. 2022M"obius Convolutions for Spherical CNNscited by 13
  27. 2022Machine learning and invariant theorycited by 13
  28. 2023Lie Group Decompositions for Equivariant Neural Networkscited by 12
  29. 2024RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentationcited by 12
  30. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11
  31. 2022Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learningcited by 10
  32. 2023Approximately Equivariant Quantum Neural Network for p4m Group Symmetries in Imagescited by 10
  33. 2024Weisfeiler Leman for Euclidean Equivariant Machine Learningcited by 10
  34. 2023Exploiting Code Symmetries for Learning Program Semanticscited by 9
  35. 2024Approximate Equivariance in Reinforcement Learningcited by 9
  36. 2021Particle Convolution for High Energy Physicscited by 8
  37. 2022Deep Neural Network Approximation of Invariant Functions through Dynamical Systemscited by 8
  38. 2022Analysis of (sub-)Riemannian PDE-G-CNNscited by 8

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