Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to identify further topological and geometric structures with which these use cases can be made accessible to machine learning. There are various techniques, such as spectral convolution, that form the basic building blocks for some convolutional neural network-like architectures on non-Euclidean data. In this paper, the concept of spectral convolution on orbifolds is introduced. This provides a building block for making learning on orbifold structured data accessible using GDL. The theory discussed is illustrated using an example from music theory.

翻译：几何深度学习（GDL）致力于研究超越欧几里得结构的数据域上的监督学习问题，例如具有图结构或流形结构的数据。由于应用相关数据的需求不断增长，有必要识别更多拓扑与几何结构，以便使机器学习能够处理这些实际用例。现有多种技术（例如谱卷积）构成了非欧几里得数据上类卷积神经网络架构的基础构建模块。本文引入了轨道流形上谱卷积的概念，为利用几何深度学习处理轨道流形结构数据提供了一个基础构建模块。文中结合音乐理论中的实例对所讨论的理论进行了阐释。