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的表示学习方法，使表示对数据的对称性具有等变性。核心思想是将潜在空间分解为一个不变因子和对称群本身，二者在语义上分别对应内在数据类别和位姿。该学习器利用相对对称性信息的监督，通过鼓励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，能够保证表示具有无损性、可解释性和解耦性。我们通过对具有多种对称性的数据集进行实验研究，结果表明我们的表示能够捕捉数据的几何结构，并在性能上优于其他等变表示学习框架。