Georgia Institute of Technology College of Sciences

Geometry arises in myriad ways within machine learning and related areas. I this talk I will focus on settings 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 existing methods better (e.g., SGD, eigenvector computation, etc.).

Ultimately, I hope to offer the audience some insights into geometric thinking and share with them some new tools that help us design, understand, and analyze models and algorithms. To make the discussion concrete I will recall a few foundational results arising from our research, provide several examples, and note some open problems.

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Bio: Suvrit Sra is a Alexander von Humboldt Professor of Artificial Intelligence at the Technical University of Munich (Germany), and and 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 machine learning. 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 AI+logistics startup.

The notion of $S$-labeling, where $S$ is a subset of the symmetric group, is a common generalization of signed $k$-coloring, signed $\mathbb{Z}_k$-coloring, DP (or Correspondence) coloring, group coloring, and coloring of gained graphs that was introduced in 2019 by Jin, Wong, and Zhu.  In this talk we use a well-known theorem of  Alon and F\"{u}redi to present an algebraic technique for bounding the number of colorings of an $S$-labeled graph from below.  While applicable in the broad context of counting colorings of $S$-labeled graphs, we will focus on the case where $S$ is a symmetric group, which corresponds to DP-coloring (or, correspondence coloring) of graphs, and the case where $S$ is a set of linear permutations which is applicable to the coloring of signed graphs, etc.

This technique allows us to prove exponential lower bounds on the number of colorings of any $S$-labeling of graphs that satisfy certain sparsity conditions. We apply these to give exponential lower bounds on the number of DP-colorings (and consequently, number of  list colorings, or usual colorings) of families of planar graphs, and on the number of colorings of families of signed (planar) graphs. These lower bounds either improve previously known results, or are first known such results.

This joint work with Samantha Dahlberg and Jeffrey Mudrock.

Join us as we define a whole new algebraic structure, starting from the axioms of the projective plane. This seminar will be aimed at students who have never seen this material and will focus on hands-on constructions of classic (and new!) algebraic structures that can arise from a projective plane. The goal of this seminar is to expose you to Desargues's theorem and hopefully even examine non-Desarguesian planes.

 This talk is a summary of a summary. We will be going over Jen Hom's 2024 Levi L. Conant Prize Winning Article "Getting a handle on the Conway knot," which discusses Lisa Piccirillo's renowned 2020 paper proving the Conway knot is not slice. In this presentation, we will go over what it means for a knot to be slice, past attempts to classify the Conway knot with knot invariants, and Piccirillo's approach of constructing a knot with the same knot trace as the Conway knot. This talk is designed for all audiences and NO prior knowledge of topology or knot theory is required. Trust me, I'm (k)not a topologist.