A Lorentz-Equivariant Transformer for All of the LHC
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Abstract (arXiv)
We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures.
Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 35 of its 85 references that are in the map. First posted on arXiv 1 Nov 2024.
Builds on
35 of 85 references.
References · 35
- 2017Attention Is All You Needcited by 59,932
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2022Flow Matching for Generative Modelingcited by 5,426
- 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,611
- 2016Gaussian Error Linear Units (GELUs)cited by 3,431
- 2017Deep Setscited by 1,394
- 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
- 2020On Layer Normalization in the Transformer Architecturecited by 906
- 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
- 2023Symbolic Discovery of Optimization Algorithmscited by 423
23 more
- 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
- 2022Particle Transformer for Jet Taggingcited by 95
- 2018Energy Flow Networks: Deep Sets for Particle Jetscited by 83
- 2017CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networkscited by 78
- 2019ParticleNet: Jet Tagging via Particle Cloudscited by 64
- 2023Clifford Group Equivariant Neural Networkscited by 54
- 2023Geometric Algebra Transformercited by 46
- 2015Jet-Images -- Deep Learning Editioncited by 41
- 2024Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physicscited by 36
- 2024CaloChallenge 2022: A Community Challenge for Fast Calorimeter Simulationcited by 34
- 2019How to GAN away Detector Effectscited by 28
- 2019LHC analysis-specific datasets with Generative Adversarial Networkscited by 26
- 2022PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physicscited by 26
- 2017QCD-Aware Recursive Neural Networks for Jet Physicscited by 22
- 2023End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physicscited by 22
- 2023Explainable Equivariant Neural Networks for Particle Physics: PELICANcited by 22
- 2022An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative trainingcited by 20
- 2023CaloClouds II: Ultra-Fast Geometry-Independent Highly-Granular Calorimeter Simulationcited by 20
- 2024The Landscape of Unfolding with Machine Learningcited by 20
- 2023Improving Generative Model-based Unfolding with Schr"odinger Bridgescited by 13
- 2023Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformerscited by 12
- 2021Optimising simulations for diphoton production at hadron colliders using amplitude neural networkscited by 9
- 2024Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoodscited by 5
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Citing papers per year: 2024: 2; 2025: 15; 2026: 10.
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- 2025Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Modelscited by 14
- 2025OmniJet-αC: Learning point cloud calorimeter simulations using generative transformerscited by 14
- 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
- 2026Neural Scaling Laws for Boosted Jet Taggingcited by 11
- 2025Foundation models for high-energy physicscited by 10
- 2025CaloHadronic: a diffusion model for the generation of hadronic showerscited by 8
- 2024Generative Unfolding with Distribution Mappingcited by 6
- 2025RINO: Renormalization Group Invariance with No Labelscited by 6
- 2026Scaling laws for amplitude surrogatescited by 5
- 2025Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learningcited by 3
- 2025Forecasting Generative Amplificationcited by 3
- 2025Enhancing next token prediction based pre-training for jet foundation modelscited by 3
15 more
- 2026AllShowers: One model for all calorimeter showerscited by 3
- 2024Extrapolating Jet Radiation with Autoregressive Transformerscited by 2
- 2025Stable and Interpretable Jet Physics with IRC-Safe Equivariant Feature Extractioncited by 2
- 2025A First Full Physics Benchmark for Highly Granular Calorimeter Surrogatescited by 2
- 2026Approximate Equivariance via Projection-based Regularisationcited by 2
- 2025Generating particle physics Lagrangians with transformerscited by 1
- 2025BitHEP -- The Limits of Low-Precision ML in HEPcited by 1
- 2025Latent Representation Learning in Heavy-Ion Collisions with MaskPoint Transformercited by 1
- 2026jBOT: Semantic Jet Representation Clustering Emerges from Self-Distillationcited by 1
- 2026Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problemscited by 1
- 2026Unknown Unknowns: Model Misspecification in Machine Learning for Physicscited by 1
- 2025Learnable cut flow for high energy physicscited by 0
- 2026Softly Induced Functional Simplicity: Implications for Neural Network Generalisation, Robustness, and Distillationcited by 0
- 2026Event Generation with Parallel Langevin Sampling and Learned Stein Diagnosticscited by 0
- 2026Machine learning for the LHC physics program: a 2025-2026 stocktakecited by 0
- 2026Machine learning for the LHC physics program: a 2025-2026 stocktake26 Sep 2026
- 2026Unknown Unknowns: Model Misspecification in Machine Learning for Physics13 Aug 2026
- 2026Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics12 Jun 2026
- 2026Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems21 May 2026
- 2026Neural Scaling Laws for Boosted Jet Tagging17 Feb 2026
- 2026Scaling laws for amplitude surrogates19 Jan 2026
- 2026jBOT: Semantic Jet Representation Clustering Emerges from Self-Distillation16 Jan 2026
- 2026AllShowers: One model for all calorimeter showers16 Jan 2026
- 2026Softly Induced Functional Simplicity: Implications for Neural Network Generalisation, Robustness, and Distillation10 Jan 2026
- 2026Approximate Equivariance via Projection-based Regularisation8 Jan 2026
- 2025Enhancing next token prediction based pre-training for jet foundation models3 Dec 2025
- 2025A First Full Physics Benchmark for Highly Granular Calorimeter Surrogates21 Nov 2025
15 more
- 2025Latent Representation Learning in Heavy-Ion Collisions with MaskPoint Transformer8 Oct 2025
- 2025Stable and Interpretable Jet Physics with IRC-Safe Equivariant Feature Extraction26 Sep 2025
- 2025Foundation models for high-energy physics25 Sep 2025
- 2025Forecasting Generative Amplification9 Sep 2025
- 2025RINO: Renormalization Group Invariance with No Labels9 Sep 2025
- 2025Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning8 Jul 2025
- 2025CaloHadronic: a diffusion model for the generation of hadronic showers26 Jun 2025
- 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant26 May 2025
- 2025BitHEP -- The Limits of Low-Precision ML in HEP4 Apr 2025
- 2025Learnable cut flow for high energy physics28 Mar 2025
- 2025Generating particle physics Lagrangians with transformers16 Jan 2025
- 2025OmniJet-αC: Learning point cloud calorimeter simulations using generative transformers9 Jan 2025
- 2025Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Models9 Jan 2025
- 2024Extrapolating Jet Radiation with Autoregressive Transformers16 Dec 2024
- 2024Generative Unfolding with Distribution Mapping4 Nov 2024
- 2025Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Modelscited by 14
- 2025OmniJet-αC: Learning point cloud calorimeter simulations using generative transformerscited by 14
- 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
- 2026Neural Scaling Laws for Boosted Jet Taggingcited by 11
- 2025Foundation models for high-energy physicscited by 10
- 2024Generative Unfolding with Distribution Mappingcited by 6
- 2025RINO: Renormalization Group Invariance with No Labelscited by 6
- 2026Scaling laws for amplitude surrogatescited by 5
- 2025Forecasting Generative Amplificationcited by 3
- 2025Enhancing next token prediction based pre-training for jet foundation modelscited by 3
- 2026AllShowers: One model for all calorimeter showerscited by 3
- 2024Extrapolating Jet Radiation with Autoregressive Transformerscited by 2
12 most cited of 25 All 25 (JSON)
- 2026Machine learning for the LHC physics program: a 2025-2026 stocktake26 Sep 2026
- 2026Unknown Unknowns: Model Misspecification in Machine Learning for Physics13 Aug 2026
- 2026Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics12 Jun 2026
- 2026Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems21 May 2026
- 2026Neural Scaling Laws for Boosted Jet Tagging17 Feb 2026
- 2026Scaling laws for amplitude surrogates19 Jan 2026
- 2026jBOT: Semantic Jet Representation Clustering Emerges from Self-Distillation16 Jan 2026
- 2026AllShowers: One model for all calorimeter showers16 Jan 2026
- 2026Softly Induced Functional Simplicity: Implications for Neural Network Generalisation, Robustness, and Distillation10 Jan 2026
- 2026Approximate Equivariance via Projection-based Regularisation8 Jan 2026
- 2025Enhancing next token prediction based pre-training for jet foundation models3 Dec 2025
- 2025A First Full Physics Benchmark for Highly Granular Calorimeter Surrogates21 Nov 2025
12 newest of 25 All 25 (JSON)