Geometric Deep Learning: Going beyond Euclidean data

This paper addresses the challenge of applying deep learning to data with an underlying non-Euclidean structure. It notes that many scientific fields study such data, including 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, and that this geometric data is often large and complex, in the case of social networks on the scale of billions, making it a natural target for machine learning techniques.

The authors observe that while deep neural networks have recently proven to be powerful tools for a broad range of problems in computer vision, natural language processing, and audio analysis, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of those structures are built into the networks used to model them. This motivates the effort to go beyond Euclidean data toward geometric deep learning on non-Euclidean domains.