Geometric Deep Learning: Going beyond Euclidean data

This paper surveys geometric deep learning, motivated by the observation that many scientific fields study data with an underlying non-Euclidean structure, such as social networks in computational social science, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. Such geometric data are often large and complex, in some cases at the scale of billions of elements, making them natural targets for machine learning techniques including deep neural networks.

The authors note that deep neural networks have recently proven powerful across computer vision, natural language processing, and audio analysis, but have been most successful on data with an underlying Euclidean or grid-like structure where the relevant invariances are built into the network architectures. The paper's importance lies in framing and reviewing how to extend these successful deep learning tools to non-Euclidean domains, laying groundwork for methods on graphs and manifolds.