Detecting Symmetries with Neural Networks
This work addresses the challenge of symmetry detection for researchers in fields like physics and mathematics, though it appears incremental as it builds on existing neural network techniques.
The paper tackles the problem of identifying symmetries in datasets, which is crucial for efficient data handling, by presenting a neural network method that detects symmetries and their orbits, and demonstrates its application in classifying Calabi-Yau manifolds with a novel graph-based data representation.
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.