几何深度学习：超越欧几里得数据
Geometric deep learning: going beyond Euclidean data
摘要：
许多科学领域研究具有非欧几里德空间的底层结构的数据。一些例子包括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、遗传学中的调节网络和计算机图形学中的网格表面。在许多应用中，这样的几何数据是大而复杂的（在社交网络的情况下，在数十亿的规模上），并且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，最近已被证明是解决计算机视觉、自然语言处理和音频分析等广泛问题的强大工具。然而，这些工具在具有底层欧几里得或网格状结构的数据上最为成功，并且在这些结构的不变性被构建到用于对其进行建模的网络中的情况下。几何深度学习是新兴技术的总称，这些新兴技术试图将（结构化）深度神经模型推广到非欧几里德域，如图和流形。本文的目的是概述几何深度学习问题的不同示例，并在这个新兴领域提出可用的解决方案，关键难点，应用和未来的研究方向。
英文摘要：
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.
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