Inverse Problems on graphs encompass many areas of physics, algorithms and statistics, and are a confluence of powerful methods, ranging from computational harmonic analysis and high-dimensional statistics to statistical physics. Similarly as with inverse problems in signal processing, learning has emerged as an intriguing alternative to regularization and other computationally tractable relaxations, opening up new questions in which high-dimensional optimization, neural networks and data play a prominent role. In this talk, I will argue that several tasks that are ‘geometrically stable’ can be well approximated with Graph Neural Networks, a natural extension of Convolutional Neural Networks on graphs. I will present recent work on supervised community detection, quadratic assignment, neutrino detection and beyond showing the flexibility of GNNs to extend classic algorithms such as Belief Propagation.

Bio: Joan Bruna is an Assistant Professor of Computer Science, Data Science and Mathematics (affiliated) at the Courant Institute of Mathematical Sciences, New York University, and at the Center for Data Science. His research interests touch several areas of Machine Learning, Signal Processing and High-Dimensional Statistics. In particular, in the past few years he has been working on Convolutional Neural Networks, studying some of its theoretical properties, extensions to more general geometries, and applications to physical sciences and statistics. Before that, he worked at FAIR (Facebook AI Research) in New York. Prior to that, he was a postdoctoral researcher at Courant Institute, NYU. He completed his PhD in 2013 at Ecole Polytechnique, France. He is the recipient of an Alfred. P. Sloan Fellowship (2018), and he has organized multiple tutorials and workshops on geometric deep learning, including NIPS and CVPR in 2017.