AtlasD: Automatic Local Symmetry Discovery

• URL: http://arxiv.org/abs/2504.10777v1
• Date: Tue, 15 Apr 2025 00:41:55 GMT
• Title: AtlasD: Automatic Local Symmetry Discovery
• Authors: Manu Bhat, Jonghyun Park, Jianke Yang, Nima Dehmamy, Robin Walters, Rose Yu,
• Abstract summary: This paper formalizes the notion of local symmetry as atlas equivariance.<n>Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks.<n>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.
• Score: 27.793766164323532
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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