Papers › Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant

Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant

26 May 2025arXiv:2505.20280archive 2025-07-28

Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred A. 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× faster and using $5$-100× fewer FLOPs.

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