论文标题
检测与神经网络的对称性
Detecting Symmetries with Neural Networks
论文作者
论文摘要
在数据集中识别对称性通常很困难，但是对它们的知识对于有效的数据处理至关重要。在这里，我们提出了一种方法，如何使用神经网络来识别对称性。我们在神经网络的嵌入层中广泛使用结构，这使我们能够确定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的对称组，我们分析了输入中的不变轨道。我们介绍了基于旋转组$ so（n）$和统一组$ su（2）的示例。$进一步我们发现，此方法对于完整交点Calabi-yau流形的分类很有用，在该分类中，在输入空间上识别离散对称性至关重要。在此示例中，我们在图表方面介绍了新的数据表示。
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.
