ATLAS: Automatic Local Symmetry Discovery
Keywords: local symmetry discovery, symmetry discovery, equivariance, gauge equivariant neural network, Lie theory
TL;DR: A symmetry discovery method capable of learning local transformations.
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 (ATLAS), 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 ATLAS 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.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 7821
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