将谱卷积拓展到轨道流形，让几何深度学习可处理更复杂的非欧数据。
Spectral Convolution on Orbifolds for Geometric Deep Learning
- 提出在轨道流形上定义谱卷积的新方法
- 首次实现对轨道结构数据的几何深度学习建模
- 适用于音乐理论等具有复杂对称性的领域
几何深度学习（GDL）处理超越欧几里得结构的数据域，如图或流形结构数据。随着应用需求增长，需要识别更多拓扑与几何结构，使这些数据可被机器学习利用。现有技术如谱卷积是构建非欧数据卷积神经网络的基础模块。本文引入轨道流形上的谱卷积概念，为在轨道结构数据上进行学习提供基础工具。所提理论通过音乐理论中的一个例子进行说明。
原文摘要 · Abstract (English)
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.
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