Please join us this FRIDAY, OCTOBER 29TH FOR OUR NEXT SEMINAR BY DR. JOHN WRIGHT, ASSOCIATE PROFESSOR OF ELECTRICAL ENGINEERING AT COLUMBIA UNIVERSITY. THE PRESENTATION WILL BEGIN AT 1:00PM VIA ZOOM:

https://ucdavis.zoom.us/j/92000635042?pwd=aEYzZzc3L09JR0ZuTHFkblFob2V1QT09

MEETING ID: 920 0063 5042

PASSCODE: 902130

DR. WRIGHT’S SEMINAR WILL BE FOLLOWED IMMEDIATELY BY DISCUSSIONS FROM 2:00-4:00PM. PLEASE USE THE FOLLOWING GOOGLE DOCS LINK TO SIGN UP FOR A

30 MINUTE TIME SLOT:

https://docs.google.com/spreadsheets/d/1hOWeKHcBF_Sp4_XqkSp4-6Zt0VmHWQaMDRNiEfCZyNY/edit?usp=sharing

ABSTRACT: Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure--a binary classification task that uses a deep fully-connected neural network to classify data drawn from two disjoint smooth curves on the unit sphere. Aside from mild regularity conditions, we place no restrictions on the configuration of the curves. We prove that when (i) the network depth is large relative to certain geometric properties that set the difficulty of the problem and (ii) the network width and number of samples is polynomial in the depth, randomly-initialized gradient descent quickly learns to correctly classify all points on the two curves with high probability. To our knowledge, this is the first generalization guarantee for deep networks with nonlinear data that depends only on intrinsic data properties. Our analysis draws on ideas from harmonic analysis and martingale concentration for handling statistical dependencies in the initial (random) network. We sketch applications to invariant vision, and to gravitational wave astronomy, where leveraging low-dimensional structure leads to statistically optimal tests for identifying signals in noise.

Joint work with Sam Buchanan, Dar Gilboa, Tim Wang, Jingkai Yan

BIO: John Wright is an associate professor in Electrical Engineering at Columbia University. He is also affiliated with the Department of Applied Physics and Applied Mathematics and Columbia's Data Science Institute. He received his PhD in Electrical Engineering from the University of Illinois at Urbana Champaign in 2009. Before joining Columbia, he was with Microsoft Research Asia from 2009-2011. His research interests include sparse and low-dimensional models for high-dimensional data, optimization (convex and otherwise), and applications in imaging and vision.