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

• URL: http://arxiv.org/abs/2505.20280v1
• Date: Mon, 26 May 2025 17:57:17 GMT
• Title: Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant
• Authors: Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred A. Hamprecht,
• Abstract summary: Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics.<n>We introduce Lorentz Local Canonicalization (LLoCa), a general framework that renders any backbone network exactly Lorentz-equivariant.<n>Our models surpass state-of-the-art accuracy on relevant particle physics tasks, while being $4times$ faster and using $5$-$100times$ fewer FLOPs.
• Score: 12.763777716363016
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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