AtlasD: Automatic Local Symmetry Discovery
This addresses the limitation of symmetry discovery for researchers in fields like physics and computer vision by providing a method to identify local symmetries, though it is incremental as it builds on existing symmetry concepts.
The paper tackled the problem of existing symmetry discovery methods focusing only on global transformations and missing local symmetries, which can misrepresent true symmetry, by proposing AtlasD to automatically discover local symmetries through atlas equivariance, demonstrating its ability to recover local symmetry groups in top-quark tagging and PDE experiments and showing it improves performance in climate segmentation and vision tasks.
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.