Geometric deep learning: going beyond Euclidean data

TL;DR

This paper reviews the emerging field of geometric deep learning, which extends neural network techniques to non-Euclidean data like graphs and manifolds, addressing complex structures in various scientific domains.

Contribution

It provides an overview of geometric deep learning problems, solutions, challenges, applications, and future research directions in this nascent field.

Findings

Geometric deep learning generalizes neural networks to non-Euclidean domains.

Applications include social networks, brain imaging, and computer graphics.

Key challenges involve handling large, complex, and irregular data structures.

Abstract

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.