We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

翻译：我们提出了一种通用方法，用于学习对数据对称性具有等变性的表示。核心思想是将潜空间分解为一个不变因子与对称群本身，其分量在语义上分别对应内在数据类别和姿态。该学习器基于相对对称性信息的监督，通过一个促进等变性的损失函数进行训练。该方法受群论理论结果的启发，能够保证生成无损、可解释且解耦的表示。我们通过涉及多种对称性数据集的实验进行了实证研究。结果表明，我们的表示捕获了数据的几何结构，且性能优于其他等变表示学习框架。