Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant
Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred Hamprecht
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 to 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 surpass state-of-the-art accuracy on relevant particle physics tasks, while being $4\times$ faster and using $5$-$100\times$ fewer FLOPs.