Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant
Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred A. Hamprecht
Abstract
Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics. Current implementations rely on specialized layers, limiting architectural choices. We introduce Lorentz Local Canonicalization (LLoCa), a general framework that renders any backbone network exactly Lorentz-equivariant. Using equivariantly predicted local reference frames, we construct LLoCa-transformers and graph networks. We adapt a recent approach for geometric message passing to the non-compact Lorentz group, allowing propagation of space-time tensorial features. Data augmentation emerges from LLoCa as a special choice of reference frame. Our models achieve competitive and state-of-the-art accuracy on relevant particle physics tasks, while being $4\times$ faster and using $10\times$ fewer FLOPs.
BibTeX
@inproceedings{
spinner2025lorentz,
title={Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant},
author={Jonas Spinner and Luigi Favaro and Peter Lippmann and Sebastian Pitz and Gerrit Gerhartz and Tilman Plehn and Fred A. Hamprecht},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=2xeYuWd7WZ}
}