Geometric deep learning: going beyond Euclidean data
打开互动全文版（逐段中英对照 + 图/公式 + 论文问答）→许多科学领域研究的数据具有非欧几里得空间的底层结构。例如，计算社会科学中的社交网络、通信中的传感器网络、脑成像中的功能网络、遗传学中的调控网络以及计算机图形学中的网格表面。在许多应用中，这些几何数据规模大且复杂（社交网络可达数十亿量级），是机器学习技术的自然目标。特别是，我们希望使用深度神经网络，该网络最近在计算机视觉、自然语言处理和音频分析等广泛问题上展现了强大的能力。然而，这些工具最擅长处理具有欧几里得或网格状结构的数据，并且在这些结构的等变性被内置于建模网络中的情况下表现最佳。几何深度学习是一个总称，涵盖了将（结构化）深度神经模型推广到非欧几里得域（如图和流形）的新兴技术。本文旨在概述几何深度学习问题的不同实例，并介绍该新兴领域中现有的解决方案、关键难点、应用及未来研究方向。
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.