Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics
<|reference_start|>Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics: 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.<|reference_end|>
@article{spinner2024lorentz-equivariant,
    title={Lorentz-Equivariant Geometric Algebra Transformers for High-Energy
  Physics},
    author={Jonas Spinner, Victor Bres'o, Pim de Haan, Tilman Plehn, Jesse
  Thaler, Johann Brehmer},
    journal={arXiv preprint arXiv:2405.14806},
    year={2024},
    number={MIT-CTP/5723},
    archivePrefix={arXiv},
    eprint={2405.14806},
    primaryClass={physics.data-an cs.LG hep-ph stat.ML}
}