Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915348581711872 |
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| author | Spinner, Jonas Bresó, Victor de Haan, Pim Plehn, Tilman Thaler, Jesse Brehmer, Johann |
| author_facet | Spinner, Jonas Bresó, Victor de Haan, Pim Plehn, Tilman Thaler, Jesse Brehmer, Johann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics Spinner, Jonas Bresó, Victor de Haan, Pim Plehn, Tilman Thaler, Jesse Brehmer, Johann Data Analysis, Statistics and Probability Machine Learning High Energy Physics - Phenomenology 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. |
| title | Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics |
| topic | Data Analysis, Statistics and Probability Machine Learning High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2405.14806 |