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.

本文介绍了一种使用神经网络来识别数据集中对称性的方法，并利用嵌入层的结构来识别对称性是否存在以及在输入中对称性的轨道。通过分析输入中的不变轨道，确定所存在的连续或离散对称群，并使用图表述的方式对完全交空间卡拉比 - 雅莫夫流形进行分类，并发现该方法对于识别输入空间中的离散对称性至关重要。