A Lorentz-Equivariant Transformer for All of the LHC

2024-11-01

arXiv.org

AI Summary

The lack of Lorentz covariance in existing machine learning models severely limits their generalization in high-energy physics. Method: We propose the Lorentz-covariant Geometric Algebra Transformer (L-GATr), a strictly Lorentz-equivariant Transformer architecture built within the spacetime geometric algebra framework, where particle four-momenta serve as inputs. To our knowledge, this is the first work to achieve a unified Lorentz-covariant design across all major high-energy physics tasks—amplitude regression, jet classification, and generative modeling—while supporting controllable symmetry breaking. Geometric algebra representations and equivariant embeddings jointly enable both discriminative and generative capabilities. Contribution/Results: L-GATr achieves state-of-the-art performance on all three LHC benchmark tasks, significantly outperforming prior methods. These results empirically validate that explicit Lorentz-covariant inductive biases yield consistent, substantial gains across diverse high-energy physics machine learning applications.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Achieving Lorentz-equivariance in machine learning for LHC physics
• Improving performance on amplitude regression and jet classification tasks
• Developing first Lorentz-equivariant generative network for particle physics

Innovation

• Lorentz-Equivariant Geometric Algebra Transformer architecture
• Scalable transformer handling Lorentz transformations equivariance
• Versatile architecture capable of breaking symmetries when needed