Title: Benefits of learning with symmetries: eigenvectors, graph representations and sample complexity
Abstract: In many applications, especially in the sciences, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes, while it also poses challenges on efficient model design.
In the first part of the talk, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important, for instance, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances or equivariances – sign flips and changes of basis – and their theoretical and empirical benefits.
Second, we will take a broader, theoretical perspective. Empirically, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to a wide range of group actions.
This talk is based on joint work with Joshua Robinson, Derek Lim, Behrooz Tahmasebi, Lingxiao Zhao, Tess Smidt, Suvrit Sra and Haggai Maron.
Bio: Stefanie Jegelka is a Humboldt Professor at TU Munich and an Associate Professor in the Department of EECS at MIT. Before joining MIT, she was a postdoctoral researcher at UC Berkeley, and obtained her PhD from ETH Zurich and the Max Planck Institute for Intelligent Systems. Stefanie has received a Sloan Research Fellowship, an NSF CAREER Award, a DARPA Young Faculty Award, the German Pattern Recognition Award, a Best Paper Award at ICML and an invitation as sectional lecturer at the International Congress of Mathematicians. She has co-organized multiple workshops on (discrete) optimization in machine learning and graph representation learning, and has served as an Action Editor at JMLR and a program chair of ICML 2022. Her research interests span the theory and practice of algorithmic machine learning, in particular, learning problems that involve combinatorial, algebraic or geometric structure.