[2406.07598] Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency

Computer Science > Machine Learning arXiv:2406.07598 (cs) [Submitted on 11 Jun 2024 (v1), last revised 24 Mar 2026 (this version, v5)] Title:Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency Authors:Yuchao Lin, Jacob Helwig, Shurui Gui, Shuiwang Ji View a PDF of the paper titled Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency, by Yuchao Lin and 3 other authors View PDF HTML (experimental) Abstract:We consider achieving equivariance in machine learning systems via frame averaging. Current frame averaging methods involve a costly sum over large frames or rely on sampling-based approaches that only yield approximate equivariance. Here, we propose Minimal Frame Averaging (MFA), a mathematical framework for constructing provably minimal frames that are exactly equivariant. The general foundations of MFA also allow us to extend frame averaging to more groups than previously considered, including the Lorentz group for describing symmetries in space-time, and the unitary group for complex-valued domains. Results demonstrate the efficiency and effectiveness of encoding symmetries via MFA across a diverse range of tasks, including $n$-body simulation, top tagging in collider physics, and relaxed energy prediction. Our code is available at this https URL. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2406.07598 [cs.LG]   (or arXiv:2406.07598v5 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2406.07598 Focus to learn...