Geometric and Topological Representation Learning

Real-world data in natural and social sciences typically exhibit intricate and complex relationships that are well-suited to be represented as graphs, point clouds and time series among other geometric and topological structures. Embedding appropriate inductive biases into deep learning models is thus essential in building systems that can learn and generalize from such data. Machine learning on graphs in particular has seen rapid development in recent years, owing much to advances in graph representation learning (GRL), a large family of methods with close connections to signal processing designed to encode sparse graph structured data into dense vector form in graph representations. Thanks to their ability to leverage data-intrinsic geometries, graph neural networks (GNN) have been in the forefront of GRL, while later work have built upon this foundation to arrive at a wide selection of complex and powerful GNN architectures addressing expressivity, multi-resolution signals, or implicit symmetries. These developments have collectively facilitated the use of GNNs in a variety of applications ranging from recommender systems and traffic forecasting to biochemistry and materials science, while also spawning novel subfields that extend these learning paradigms to even more complex structures in temporal graphs or simplicial complexes. In this tutorial, we aim to provide a bottom-up view of modern graph representation learning and its extensions to related topological structures. Our tutorial aims to appeal to a large audience including both newcomers into the field of geometric representation learning as well as research and industry experts.