Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the structure in the embedding layer of the neural network which allows us to identify whether a symmetry is present and to identify orbits of the symmetry in the input. To determine which continuous or discrete symmetry group is present we analyse the invariant orbits in the input. We present examples based on rotation groups SO(n) and the unitary group SU(2). Further we find that this method is useful for the classification of complete intersection Calabi-Yau manifolds where it is crucial to identify discrete symmetries on the input space. For this example we present a novel data representation in terms of graphs.

通常很难确定数据集中的对称性，但是有关对称性的知识对于有效的数据处理至关重要。在这里，我们提出了一种如何使用神经网络来识别对称性的方法。我们广泛使用神经网络嵌入层中的结构，这使我们能够识别是否存在对称性，并识别输入中对称性的轨道。为了确定存在哪个连续或离散对称组，我们分析了输入中的不变轨道。我们基于旋转组SO（n）和the组SU给出示例（2）。进一步，我们发现该方法对于完整交集卡拉比-尤奥流形的分类很有用，在该分类中识别输入空间上的离散对称性至关重要。对于此示例，我们以图形的形式展示了一种新颖的数据表示形式。