AtlasD: Automatic Local Symmetry Discovery

Manu Bhat, Jonghyun Park, Jianke Yang, Nima Dehmamy, Robin Walters, Rose Yu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:4153-4171, 2025.

Abstract

Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a misrepresentation of the true symmetry. In this paper, we formalize the notion of local symmetry as atlas equivariance. Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks and then learning a Lie group basis to which the predictors are equivariant. We demonstrate AtlasD is capable of discovering local symmetry groups with multiple connected components in top-quark tagging and partial differential equation experiments. The discovered local symmetry is shown to be a useful inductive bias that improves the performance of downstream tasks in climate segmentation and vision tasks. Our code is publicly available at https://github.com/Rose-STL-Lab/AtlasD.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bhat25a, title = {{A}tlas{D}: Automatic Local Symmetry Discovery}, author = {Bhat, Manu and Park, Jonghyun and Yang, Jianke and Dehmamy, Nima and Walters, Robin and Yu, Rose}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {4153--4171}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bhat25a/bhat25a.pdf}, url = {https://proceedings.mlr.press/v267/bhat25a.html}, abstract = {Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a misrepresentation of the true symmetry. In this paper, we formalize the notion of local symmetry as atlas equivariance. Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks and then learning a Lie group basis to which the predictors are equivariant. We demonstrate AtlasD is capable of discovering local symmetry groups with multiple connected components in top-quark tagging and partial differential equation experiments. The discovered local symmetry is shown to be a useful inductive bias that improves the performance of downstream tasks in climate segmentation and vision tasks. Our code is publicly available at https://github.com/Rose-STL-Lab/AtlasD.} }
Endnote
%0 Conference Paper %T AtlasD: Automatic Local Symmetry Discovery %A Manu Bhat %A Jonghyun Park %A Jianke Yang %A Nima Dehmamy %A Robin Walters %A Rose Yu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bhat25a %I PMLR %P 4153--4171 %U https://proceedings.mlr.press/v267/bhat25a.html %V 267 %X Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a misrepresentation of the true symmetry. In this paper, we formalize the notion of local symmetry as atlas equivariance. Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks and then learning a Lie group basis to which the predictors are equivariant. We demonstrate AtlasD is capable of discovering local symmetry groups with multiple connected components in top-quark tagging and partial differential equation experiments. The discovered local symmetry is shown to be a useful inductive bias that improves the performance of downstream tasks in climate segmentation and vision tasks. Our code is publicly available at https://github.com/Rose-STL-Lab/AtlasD.
APA
Bhat, M., Park, J., Yang, J., Dehmamy, N., Walters, R. & Yu, R.. (2025). AtlasD: Automatic Local Symmetry Discovery. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:4153-4171 Available from https://proceedings.mlr.press/v267/bhat25a.html.

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