[Theory] TODAY: [TTIC Talks] 10/28 Research at TTIC: Sam Buchanan, TTIC

[Brandie Jones]

*When:*         Friday, October 28th at *12:30pm CT*


*Where:*       Talk will be given *live, in-person* at

                       TTIC, 6045 S. Kenwood Avenue

                       5th Floor, Room 530



*Virtually:*    via Panopto (Livestream
<https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=6ee5009d-1621-4a86-adcd-af180134b425>
)


*Who:*            Sam Buchanan, TTIC



*Title:*            Deep Networks and the Multiple Manifold Problem


*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, where leveraging low-dimensional structure leads to
novel resource-efficient neural network architectures for detecting
deformations of visual motifs.

***********************************************************************************************

*Presence at TTIC requires being fully vaccinated for COVID-19 or having
a TTIC or UChicago-approved exemption. Masks are optional in all common
areas. Full visitor guidance is available at ttic.edu/visitors
<http://ttic.edu/visitors>.*

***********************************************************************************************

*Research at TTIC Seminar Series*


TTIC is hosting a weekly seminar series presenting the research currently
underway at the Institute. Every week a different TTIC faculty member will
present their research.  The lectures are intended both for students
seeking research topics and advisors and for the general TTIC and
University of Chicago communities interested in hearing what their
colleagues are up to.

-- 
*Brandie Jones *
*Administrative Assistant*
Toyota Technological Institute
6045 S. Kenwood Avenue
Chicago, IL  60637
www.ttic.edu

Working Remote on Tuesdays
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