Geometric Deep Learning: Going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a\nnon-Euclidean space. Some examples include social networks in computational\nsocial sciences, sensor networks in communications, functional networks in\nbrain imaging, regulatory networks in genetics, and meshed surfaces in computer\ngraphics. In many applications, such geometric data are large and complex (in\nthe case of social networks, on the scale of billions), and are natural targets\nfor machine learning techniques. In particular, we would like to use deep\nneural networks, which have recently proven to be powerful tools for a broad\nrange of problems from computer vision, natural language processing, and audio\nanalysis. However, these tools have been most successful on data with an\nunderlying Euclidean or grid-like structure, and in cases where the invariances\nof these structures are built into networks used to model them. Geometric deep\nlearning is an umbrella term for emerging techniques attempting to generalize\n(structured) deep neural models to non-Euclidean domains such as graphs and\nmanifolds. The purpose of this paper is to overview different examples of\ngeometric deep learning problems and present available solutions, key\ndifficulties, applications, and future research directions in this nascent\nfield.\n