L-GATr documentation

The Lorentz-equivariant Geometric Algebra Transformer (L-GATr) is a multi-purpose neural architecture for high-energy physics. It uses spacetime geometric algebra representations throughout, allowing to easily construct Lorentz-equivariant layers. These layers are combined into a transformer architecture. The L-GATr-slim variant further improves efficiency by using only scalar and vector representations.

This documentation describes the lgatr package, available under https://github.com/heidelberg-hepml/lgatr.

• Quickstart L-GATr

• Quickstart L-GATr-slim

• Spacetime Geometric Algebra

• Attention Backends

• Lorentz Symmetry Breaking

• API Reference

Citation

If you find this package useful, please cite our papers:

@article{Brehmer:2024yqw,
   author = "Brehmer, Johann and Bres{\'o}, V{\'\i}ctor and de Haan, Pim and Plehn, Tilman and Qu, Huilin and Spinner, Jonas and Thaler, Jesse",
   title = "{A Lorentz-equivariant transformer for all of the LHC}",
   eprint = "2411.00446",
   archivePrefix = "arXiv",
   primaryClass = "hep-ph",
   reportNumber = "MIT-CTP/5802",
   doi = "10.21468/SciPostPhys.19.4.108",
   journal = "SciPost Phys.",
   volume = "19",
   number = "4",
   pages = "108",
   year = "2025"
}
@article{Petitjean:2025zjf,
   author = {Petitjean, Antoine and Plehn, Tilman and Spinner, Jonas and K{\"o}the, Ullrich},
   title = "{Economical Jet Taggers -- Equivariant, Slim, and Quantized}",
   eprint = "2512.17011",
   archivePrefix = "arXiv",
   primaryClass = "hep-ph",
   reportNumber = "IPPP/25/93",
   month = "12",
   year = "2025"
}
@inproceedings{spinner2025lorentz,
   title={Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics},
   author={Spinner, Jonas and Bres{\'o}, Victor and De Haan, Pim and Plehn, Tilman and Thaler, Jesse and Brehmer, Johann},
   booktitle={Advances in Neural Information Processing Systems},
   year={2024},
   volume={37},
   eprint = {2405.14806},
   url = {https://arxiv.org/abs/2405.14806}
}
@inproceedings{brehmer2023geometric,
   title = {Geometric Algebra Transformer},
   author = {Brehmer, Johann and de Haan, Pim and Behrends, S{\"o}nke and Cohen, Taco},
   booktitle = {Advances in Neural Information Processing Systems},
   year = {2023},
   volume = {36},
   eprint = {2305.18415},
   url = {https://arxiv.org/abs/2305.18415},
}