发现函数局部对称性，提升模型在气候与视觉任务中的表现。
AtlasD: Automatic Local Symmetry Discovery
- 通过训练局部预测网络并学习李群基，实现局部对称性自动发现。
- 在顶夸克标记和偏微分方程实验中成功识别出含多连通分支的局部对称群。
- 发现的局部对称性可作为有效归纳偏置，提升下游任务性能。
现有对称性发现方法主要关注整个系统或空间的全局变换，却忽略了局部邻域内的对称性，可能导致报告的对称群不能真实反映实际对称性。本文将局部对称性形式化为图集等变性（atlas equivariance）。提出的自动局部对称性发现框架 AtlasD，通过训练局部预测网络并学习使其等变的李群基，来恢复函数的局部对称性。实验表明，AtlasD 能在顶夸克标记和偏微分方程任务中发现具有多个连通分支的局部对称群。所发现的局部对称性被证明是有效的归纳偏置，能显著提升气候分割与视觉任务的下游性能。
原文摘要 · Abstract (English)
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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