[Theory] 4/11 Talks at TTIC: Sam Buchanan, Columbia University

[Mary Marre]

*When:*        Monday, April 11th at* 11:30 am CT*


*Where:*       Zoom Virtual Talk (*register in advance here
<https://uchicagogroup.zoom.us/webinar/register/WN_TkyVf0mWQjWq0a6PjUZNPg>*)


*Who: *         Sam Buchanan, Columbia University




*Title:          *Deep Networks Through the Lens of Low-Dimensional
Structure

*Abstract: *I will describe two recent works that study the interactions
between deep neural networks and data with low-dimensional geometric
structure.  First, I will discuss the multiple manifold problem, a binary
classification task that uses a deep fully-connected neural network to
classify data drawn from two disjoint submanifolds of the unit sphere.  We
obtain in this model the first end-to-end algorithmic result for guaranteed
classification of low-dimensional nonlinear manifold data with deep neural
networks, as well as essentially optimal rates of concentration for
features and gradients in randomly-initialized ReLU networks.  Second, I
will discuss a conceptual approach to deriving resource-efficient invariant
neural network architectures for computing with visual data, and
demonstrate proofs-of-concept on simple vision-inspired tasks.  Together,
these results suggest a promising approach to studying questions of
resource-efficiency and performance for deep neural networks, with
implications for practical computation.

*Bio: *Sam Buchanan is a Ph.D. candidate in the Electrical Engineering
Department at Columbia University, advised by Prof. John Wright. His
research interests include the theoretical analysis of deep neural
networks, particularly in connection with structured data, and associated
applications in machine learning and signal processing. He is a 2017 U.S.
Department of Defense NDSEG Fellow.

*Host: David McAllester <mcallester at ttic.edu>*




Mary C. Marre
Faculty Administrative Support
*Toyota Technological Institute*
*6045 S. Kenwood Avenue*
*Chicago, IL  60637*
*mmarre at ttic.edu <mmarre at ttic.edu>*
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