mlsanityData to 14 Oct 2026

Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics

arXiv 2405.14806 ↗First posted 23 May 2024physics.data-an cs.LG hep-phcited by 38

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Abstract (arXiv)

Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). Builds on 31 of its 75 references that are in the map. First posted on arXiv 23 May 2024.

Builds on

31 of 75 references.

References · 31

  1. 2017Attention Is All You Needcited by 60,361
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,673
  5. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  6. 2017Deep Setscited by 1,421
  7. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  9. 2020On Layer Normalization in the Transformer Architecturecited by 922
  10. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
  11. 2019The frontier of simulation-based inferencecited by 502
  12. 2016Revisiting Classifier Two-Sample Testscited by 268
19 more
  1. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  2. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  3. 2022Particle Transformer for Jet Taggingcited by 98
  4. 2022Clifford Neural Layers for PDE Modelingcited by 92
  5. 2018Energy Flow Networks: Deep Sets for Particle Jetscited by 84
  6. 2023Clifford Group Equivariant Neural Networkscited by 55
  7. 2015Jet-Images -- Deep Learning Editioncited by 41
  8. 2023Geometric Clifford Algebra Networkscited by 38
  9. 2018Constraining Effective Field Theories with Machine Learningcited by 26
  10. 2022PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physicscited by 26
  11. 2024Clifford-Steerable Convolutional Neural Networkscited by 25
  12. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  13. 2021Generative Networks for Precision Enthusiastscited by 21
  14. 2024The Landscape of Unfolding with Machine Learningcited by 20
  15. 2023Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformerscited by 13
  16. 2019Covariance in Physics and Convolutional Neural Networkscited by 12
  17. 2020Simulation-based inference methods for particle physicscited by 11
  18. 2021Graded Symmetry Groups: Plane and Simplecited by 11
  19. 2021Optimising simulations for diphoton production at hadron colliders using amplitude neural networkscited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 8; 2025: 12; 2026: 18.

38 papers.

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  1. 2024Does equivariance matter at scale?cited by 52
  2. 2024A Lorentz-Equivariant Transformer for All of the LHCcited by 28
  3. 2024Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flowscited by 13
  4. 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
  5. 2024Generative Unfolding with Distribution Mappingcited by 6
  6. 2025RINO: Renormalization Group Invariance with No Labelscited by 6
  7. 2025Sub-microsecond Transformers for Jet Tagging on FPGAscited by 6
  8. 2026Scaling laws for amplitude surrogatescited by 6
  9. 2024Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networkscited by 5
  10. 2024Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoodscited by 5
  11. 2024Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physicscited by 4
  12. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
26 more
  1. 2025Forecasting Generative Amplificationcited by 3
  2. 2025Enhancing next token prediction based pre-training for jet foundation modelscited by 3
  3. 2026JetParticle-JEPA: An Efficient Self-Supervised Representation Learning method for Jet Tagging in High-Energy Physicscited by 3
  4. 2024Extrapolating Jet Radiation with Autoregressive Transformerscited by 2
  5. 2025Simulation-based inference for Precision Neutrino Physics through Neural Monte Carlo tuningcited by 2
  6. 2026Approximate Equivariance via Projection-based Regularisationcited by 2
  7. 2026Statistical Properties of Training & Generalizationcited by 2
  8. 2026Interpreting "Interpretability" and Explaining "Explainability" in Machine Learning in Physicscited by 2
  9. 2026Prompting Particle Physics: Tokenized Multi-modal Foundation Models for Combinatorially Many Taskscited by 2
  10. 2025Generating particle physics Lagrangians with transformerscited by 1
  11. 2025Latent Representation Learning in Heavy-Ion Collisions with MaskPoint Transformercited by 1
  12. 2025SEAL - A Symmetry EncourAging Loss for High Energy Physicscited by 1
  13. 2026Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problemscited by 1
  14. 2025Conditional Clifford-Steerable CNNs for PDE Modelingcited by 0
  15. 2025Soft Geometric Inductive Bias for Object Centric Dynamicscited by 0
  16. 2026Comparison of Image Processing Models in Quark Gluon Jet Classificationcited by 0
  17. 2026Generative models on phase spacecited by 0
  18. 2026A Geometric Algebra-informed NeRF Framework for Generalizable Wireless Channel Predictioncited by 0
  19. 2026Inpainting physics: self-supervised learning for context-driven fluid simulationcited by 0
  20. 2026Patch Hierarchical Attention Transformer for Efficient Particle Jet Taggingcited by 0
  21. 2026Particle-Lund Multimodality in Jet Taggerscited by 0
  22. 2026What Do Lorentz-Equivariant Jet Taggers Learn?cited by 0
  23. 2026Learning Standard Model structure from LHC data with Riemannian flow matchingcited by 0
  24. 2026Rotational Equivariance in Machine Learning: A Comprehensive Tutorialcited by 0
  25. 2026Coordinate-Free Automatic Differentiationcited by 0
  26. 2026RINO: Renormalization Group Distillation with No Labelscited by 0

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  1. 2023End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics
  2. 2026Generative Modeling with Orbit-Space Particle Flow Matching
  3. 2024Masked Particle Modeling on Sets: Towards Self-Supervised High Energy Physics Foundation Models
  4. 2026Preserving Continuous Symmetry in Discrete Spaces: Geometric-Aware Quantization for SO(3)-Equivariant GNNs
  5. 2025Large Language-Geometry Model: When LLM meets Equivariance
  6. 2026Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains
  7. 2025CaloHadronic: a diffusion model for the generation of hadronic showers
  8. 2026Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds