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：我们开发了一种深层次的学习方法,用于同时发现整个标签数据集的多个非三元连续对称。对称转换和相应的生成器以完全连接的神经网络为模型,这些网络经过专门设计的损失功能的培训,确保了理想的对称性。这项工作的两个新要素是使用一个低维潜层空间和对高维或电极的变异性的一般化。该方法在MNIST数字数据集上用几个例子加以演示。