Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant

Jonas Spinner (Durham University) · Luigi Favaro (UCLouvain CP3) · Peter Lippmann (Heidelberg University) · Sebastian Pitz (ITP, University Heidelberg) · Gerrit Gerhartz (Heidelberg University) · Tilman Plehn (Heidelberg) · Fred Hamprecht (Heidelberg University)

architectural choicesbackbone networkdata augmentationequivariantly predicted local reference framesflopsgeometric message passinggraph networkslloca-transformerslorentz local canonicalizationlorentz-equivariant neural networksnon-compact lorentz groupparticle physics tasksreference framespace-time tensorial featuresstate-of-the-art accuracy

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.