无需标注，自动发现数据中的隐藏对称性并显式表达。
SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservation
- 通过信息论损失函数联合建模对称性与局部性，实现稳定学习。
- 能从近似平移对称的数据中提取精确的像素平移算子。
- 适合需要挖掘复杂隐式对称性的研究人员使用。
我们提出一种新的无监督对称性学习方法，从原始数据出发，可识别底层李群对称性的最小生成元，并生成对称等变的数据表示，使隐藏对称性变为显式。该方法能从仅有近似平移对称性的数据集中学习出精确的像素平移算子，并发现肉眼难以察觉的多种复杂对称性。其核心是基于信息论的损失函数，同时衡量候选对称生成元下的数据对称程度与样本局部性，后者与对称性紧密耦合。结合用于熵估计的优化技术，该系统具备稳定性与可复现性。
原文摘要 · Abstract (English)
We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the hidden symmetry into an explicit one. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry and can learn quite different types of symmetries that are not apparent to the naked eye. The method is based on the formulation of an information-theoretic loss function that measures both the degree of symmetry of a dataset under a candidate symmetry generator and a proposed notion of locality of the samples, which is coupled to symmetry. We demonstrate that this coupling between symmetry and locality, together with an optimization technique developed for entropy estimation, results in a stable system that provides reproducible results.
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