Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency

Yuchao Lin, Jacob Helwig, Shurui Gui, Shuiwang Ji
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:30042-30079, 2024.

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 https://github.com/divelab/MFA.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-lin24i, title = {Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency}, author = {Lin, Yuchao and Helwig, Jacob and Gui, Shurui and Ji, Shuiwang}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {30042--30079}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/lin24i/lin24i.pdf}, url = {https://proceedings.mlr.press/v235/lin24i.html}, 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 https://github.com/divelab/MFA.} }
Endnote
%0 Conference Paper %T Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency %A Yuchao Lin %A Jacob Helwig %A Shurui Gui %A Shuiwang Ji %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-lin24i %I PMLR %P 30042--30079 %U https://proceedings.mlr.press/v235/lin24i.html %V 235 %X 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 https://github.com/divelab/MFA.
APA
Lin, Y., Helwig, J., Gui, S. & Ji, S.. (2024). Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:30042-30079 Available from https://proceedings.mlr.press/v235/lin24i.html.

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