<div dir="ltr"><div class="gmail_default"><div><font face="georgia, serif" color="#000000"><b>When:</b>         Friday, October 28th at <span style="background-color:rgb(255,255,0)"><b>12:30pm CT</b></span></font></div><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> <br><b>Where:</b><b>  </b>     Talk will be given <font style="font-weight:bold"><u style="background-color:rgb(255,255,0)">live, in-person</u></font><font style="font-weight:bold"> </font>at</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                       TTIC, 6045 S. Kenwood Avenue</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                       5th Floor, Room 530<b>              </b>   </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><b>Virtually:</b>    via Panopto (<a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=6ee5009d-1621-4a86-adcd-af180134b425" target="_blank">Livestream</a>) </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><br></font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><b>Who:</b><b> </b>           Sam Buchanan, TTIC</font></p><table border="0" cellspacing="0" cellpadding="0" width="0" style="width:0in;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;border-collapse:collapse"><tbody><tr><td style="padding:0in"></td></tr></tbody></table><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><b>Title:</b><b> </b>           Deep Networks and the Multiple Manifold Problem</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><font face="georgia, serif" color="#000000"><br></font></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><b>Abstract:    </b>Data with low-dimensional nonlinear structure are ubiquitous in engineering and</font></p><font color="#000000" face="georgia, serif">scientific problems. We study a model problem with such structure: a binary<br>classification task that uses a deep fully-connected neural network to classify<br>data drawn from two disjoint smooth curves on the unit sphere. Aside from mild<br>regularity conditions, we place no restrictions on the configuration of the<br>curves. We prove that when (i) the network depth is large relative to certain<br>geometric properties that set the difficulty of the problem and (ii) the<br>network width and number of samples is polynomial in the depth,<br>randomly-initialized gradient descent quickly learns to correctly classify all<br>points on the two curves with high probability. To our knowledge, this is the<br>first generalization guarantee for deep networks with nonlinear data that<br>depends only on intrinsic data properties. Our analysis draws on ideas from<br>harmonic analysis and martingale concentration for handling statistical<br>dependencies in the initial (random) network. We sketch applications to<br>invariant vision, where leveraging low-dimensional structure leads to<br>novel resource-efficient neural network architectures for detecting<br>deformations of visual motifs.</font></div><div><font color="#000000" face="georgia, serif"><br></font></div><div><div class="gmail_default"><font color="#000000" face="georgia, serif"><b>*********************************************************************************************</b></font></div><p class="MsoNormal" style="margin:0in 0in 8pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><font color="#000000" face="georgia, serif">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 <a href="http://ttic.edu/visitors" target="_blank">ttic.edu/visitors</a>.</font></b></p><p class="MsoNormal" style="margin:0in 0in 12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><font color="#000000" face="georgia, serif">*********************************************************************************************</font></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><i><font color="#000000" face="georgia, serif">Research at TTIC Seminar Series</font></i></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><div class="gmail_default"><font color="#000000" face="georgia, serif">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.</font><font face="georgia, serif" style="font-size:small"></font></div><br></div>-- <br><div dir="ltr" data-smartmail="gmail_signature"><div dir="ltr"><b style="background-color:rgb(255,255,255)"><font color="#3d85c6">Brandie Jones </font></b><div><div><i><b style="background-color:rgb(255,255,255)"><font color="#3d85c6">Administrative Assistant</font></b></i></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">Toyota Technological Institute</font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">6045 S. Kenwood Avenue</font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">Chicago, IL  60637</font></span></div></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6"><a href="http://www.ttic.edu" target="_blank">www.ttic.edu</a> </font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6"><br></font></span></div><div><font color="#3d85c6"><div style="background-color:rgb(238,238,238)">Working Remote on Tuesdays</div></font></div></div></div></div>