AI and Optimization Through a Geometric Lens

AI and optimization through a geometric lens
Abstract: Geometry arises in a myriad ways across the sciences, and quite naturally also within AI and  optimization. In this talk I wish to share with you examples where geometry helps us understand problems in machine learning, optimization, and sampling. For instance, when sampling from densities supported on a manifold, understanding geometry and the impact of curvature are crucial; surprisingly, progress on geometric sampling theory helps us understand certain generalization properties of SGD for deep-learning! Another fascinating viewpoint afforded by geometry is in non-convex optimization: geometry can either help us make training algorithms more practical (e.g., in deep learning), it can reveal tractability despite non-convexity (e.g., via geodesically convex optimization), or it can simply help us understand important ideas better (e.g., eigenvectors, LLM training, etc.).
Ultimately, my hope is to offer the audience insights into geometric thinking, and to share with them some new tools that can help us make progress on modeling, algorithms, and applications. To make my discussion concrete, I will recall a few foundational results arising from our research, provide several examples, and note some open problems. 
Bio: Suvrit Sra is an Alexander von Humboldt Professor of AI at the Technical University of Munich (Germany), and an Associate Professor of EECS at MIT (USA), where he is also a member of the Laboratory for Information and Decision Systems (LIDS) and of the Institute for Data, Systems, and Society (IDSS). He obtained his PhD in Computer Science from the University of Texas at Austin. Before TUM & MIT, he was a Senior Research Scientist at the Max Planck Institute for Intelligent Systems, Tübingen, Germany. He has held visiting positions at UC Berkeley (EECS) and Carnegie Mellon University (Machine Learning Department) during 2013-2014. His research bridges mathematical topics such as differential geometry, matrix analysis, convex analysis, probability theory, and optimization with AI. He founded the OPT (Optimization for Machine Learning) series of workshops, held from OPT2008–2017 at the NeurIPS  conference. He has co-edited a book with the same name (MIT Press, 2011). He is also a co-founder and Chief Scientist of Pendulum, a global “Decision Aware AI” startup.

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