lgatr 1.0.1

A versatile Lorentz-equivariant transformer for high-energy physics

Lorentz-Equivariant Geometric Algebra Transformer

This repository contains a minimal implementation of the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) by Jonas Spinner, Víctor Bresó, Pim de Haan, Tilman Plehn, Huilin Qu, Jesse Thaler, and Johann Brehmer. L-GATr uses spacetime geometric algebra representations to construct Lorentz-equivariant layers and combines them into a transformer architecture. You can read more about L-GATr in the following two papers:

• Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics (ML audience)
• A Lorentz-Equivariant Transformer for All of the LHC (HEP audience)

Installation

You can either install the latest release using pip

pip install lgatr

or clone the repository and install the package in dev mode

git clone https://github.com/heidelberg-hepml/lgatr.git
cd lgatr
pip install -e .

If you want a specific branch (e.g. the xformers or flex_attention branch), you can do pip install https://github.com/heidelberg-hepml/lgatr.git@basics or have a line lgatr @ https://github.com/heidelberg-hepml/lgatr.git@basics in your requirements.txt.

How to use L-GATr

1. Instantiate the LGATr class. Hyperparameters related to attention and mlp blocks are organized in dataclasses, see lgatr/layers/attention/config.py and lgatr/layers/mlp/config.py. They can be initialized using dicts or these dataclass classes.
2. Embed the network inputs into the geometric algebra using functions from lgatr/interface/. You might want to use spurions.py to break Lorentz equivariance at the input level, see Section 2.3 of the HEP paper for a discussion on symmetry breaking and when it is needed.
3. Now you're ready to push your data through the L-GATr network!

More features:

• Global LGATr design choices are controlled by the gatr_config object from lgatr/primitives/config.py.
• L-GATr supports mixed precision. The critical operations are performed in float32.
• The default branch only has the default torch attention backend. There are seperate branches for the xformers and flex_attention backends. We do not include them in the main branch yet because of their additional requirements.

Future

We are planning to extend this package in the future. If you would use them or you have more ideas, please use open an issue or a pull request.

• L-GATr transformer decoder using cross-attention.
• Add docs

Examples

• https://github.com/heidelberg-hepml/lorentz-gatr: Original LGATr implementation used for the papers
• https://github.com/spinjo/weaver-core/blob/lgatr/weaver/nn/model/LGATr.py: L-GATr in the CMS boosted object tagging library weaver

Let us know if you use lgatr, so we can add your repo to the list!

Citation

If you find this code useful in your research, please cite the following 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",
    month = "11",
    year = "2024"
}
@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},
}