We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset.

翻译：我们提出了一种深度学习方法来同时发现整个标注数据集中多个非平凡连续对称性。对称变换及相应生成元通过全连接神经网络建模，该网络使用专门构建的损失函数进行训练，以确保所需的对称性质。本工作的两个创新点在于：采用降维隐空间，并将方法推广至对高维神谕保持不变的对称变换。我们通过MNIST手写数字数据集上的多个示例演示了该方法。