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LoG 2024 (Virtual)
Wednesday November 27 2024
14:00-17:00 GMT (UK Timezone)
Overview
In recent years, there has been a surge in research at the intersection of differential geometry and generative modeling on Riemannian manifolds. Indeed the growth of applications of many highly structured data domains (e.g. graphs representing molecular data and geospatial data as points on a sphere) demand modern generative models to treat this rich anatomy of data as more than just optional inductive biases but rather as first-class citizens that drive key modeling decisions. This raises the natural question of constructing a principled playbook to imbue geometry within generative models. Geometry-aware generative models are key drivers in this space and have already started to make a substantial impact in important application areas such as diffusion and flow matching models, protein generative models, robotics, and modeling symmetries in dynamical systems. Currently, the intersection of generative modelers and geometric deep-learning communities shares a relatively small overlap compared to their parent communities. This tutorial seeks to bridge this gap by providing a bottom-up view of building modern generative models like diffusion and flow matching attuned to downstream applications that benefit from geometric inductive biases. Our tutorial is a first-of-its-kind and aims to provide a geometric blueprint for audiences that are both newcomers to generative models as well as seasoned geometric ML experts which we hope bolster both the size of the community and the potential for future advances in new theories and applications.
Table of Contents
Part 1: Primer on Diffusion/Flow Matching (Heli)
Part 2: Primer on Geometry for ML (Joey)
Part 3: Building Geometric Generative Models (Alex)
Speakers
About us
Joey Bose is a Post-Doctoral fellow at the University of Oxford and a Mila Affiliate member. He completed his PhD in Computer Science from McGill/Mila and holds a Bachelor’s and Master’s degree in Computer Engineering from the University of Toronto. His research interests span generative modeling and differential geometry for Machine Learning with a current emphasis on the foundations of geometry-aware generative models. In particular, he has been one of the first researchers to work on geometrically aware deep generative models. In addition, he was the lead organizer for the Differential Geometry meets Deep Learning (DiffGeo4DL) workshop at NeurIPS2020 and also the primary instructor for the first-ever graduate course in the world on Geometric Generative Models given at McGill University and Mila during Fall 2022.
Heli Ben-Hamu is an incoming research scientist in Fundamental Artificial Intelligence Research (FAIR) at Meta. She is a final-year PhD student advised by Yaron Lipman in the Department of Applied Math and Computer Science at the Weizmann Institute of Science. Her research broadly belongs to the fields of generative modeling and geometric deep learning, currently focusing on methodologies for generative modeling with a particular interest in gaining a deeper understanding of current methods and developing new approaches. She has given a tutorial in the Generative Modeling Summer School 2024 in TU Eindhoven and participated as an invited speaker in the 5th edition of the Generative Models and Uncertainty Quantification workshop.
Alexander Tong is an incoming assistant professor of Computer Science, Cell Biology, and Bioinformatics at Duke University. He is also currently a postdoctoral fellow with Yoshua Bengio in the Department of Computer Science and Operations Research at the Université de Montréal. He holds a Ph.D. in computer science from Yale University. He organized a Banff International Research Station (BIRS) workshop on “Deep Exploration of non-Euclidean Data with Geometric and Topological Representation Learning” in 2022, and presented a tutorial on optimal transport and flow matching models in the “Modeling and Inference of Stochastic Processes in Cells” workshop this year
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