<div dir="ltr"><div class="gmail_default" style="font-family:georgia,serif;font-size:small"><div class="gmail_default"><div class="gmail_default"><font color="#000000"><span style="letter-spacing:0.2px;white-space:pre-wrap"><font face="georgia, serif"><b>When:     </b>Wednesday, January 25th<b> at </b></font></span><b style="letter-spacing:0.2px;white-space:pre-wrap"> <span style="background-color:rgb(255,255,0)">10:30AM CT</span></b></font></div><div class="gmail_default"><b style="letter-spacing:0.2px;white-space:pre-wrap"><font face="georgia, serif" color="#000000"><br></font></b></div><div class="gmail_default"><font face="georgia, serif" color="#000000"><b style="letter-spacing:0.2px;white-space:pre-wrap">Where:    </b>Talk will be given<span style="background-color:rgb(255,255,0)"> </span><span style="background-color:rgb(255,255,0)"><font style="font-weight:bold"><u>live, in-person</u></font><font style="font-weight:bold"> </font></span>at</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">                    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"><b style="letter-spacing:0.2px;white-space:pre-wrap"><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 face="georgia, serif" color="#000000"><b style="letter-spacing:0.2px;white-space:pre-wrap">Virtually: </b><span style="letter-spacing:0.2px;white-space:pre-wrap">via Panopto (</span><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=b17f4b04-6a8f-4a69-b848-af8d00f17c6e" style="letter-spacing:0.2px;white-space:pre-wrap" target="_blank">Livestream</a><span style="letter-spacing:0.2px;white-space:pre-wrap">)</span><br></font></p><div class="gmail_default"><b style="letter-spacing:0.2px;white-space:pre-wrap"><font face="georgia, serif" color="#000000"><br></font></b></div><div class="gmail_default"><span style="letter-spacing:0.2px;white-space:pre-wrap"><font face="georgia, serif" color="#000000"><b>Who:     </b>Enric Boix, MIT</font></span></div><div class="gmail_default"><span style="letter-spacing:0.2px;white-space:pre-wrap"><font face="georgia, serif" color="#000000"><br></font></span></div><div class="gmail_default"><font color="#000000"><font face="georgia, serif"><b style="letter-spacing:0.2px;white-space:pre-wrap">Title:    </b></font></font>The staircase property and the leap complexity<font color="#000000"><font face="georgia, serif"><br style="letter-spacing:0.2px;white-space:pre-wrap"><br style="letter-spacing:0.2px;white-space:pre-wrap"><b style="letter-spacing:0.2px;white-space:pre-wrap">Abstract: </b></font></font>Which functions f : {+1,-1}^d \to \R can neural networks learn when trained with SGD? In this talk, we will consider functions that depend only on a small number of coordinates. We will study the dynamics of two-layer neural networks in the mean-field parametrization, trained by SGD with O(d) samples and will show a hierarchical property, the “merged-staircase property”, that is both necessary and nearly sufficient for learning in this setting. We will use this to propose a notion of “leap complexity” for the more general setting with O(d^c) samples. Finally, we will discuss how the necessity of a low leap complexity extends to deeper networks beyond 2 layer networks.</div><div class="gmail_default"><br></div>Joint work with Emmanuel Abbe and Theodor Misiakiewicz.<div><font face="georgia, serif" color="#000000"><br></font></div><div><div class="gmail_default"><font color="#000000"><font face="georgia, serif"><b>Bio: </b>Enric is</font></font> 4th year PhD student in the EECS department at MIT, advised by Guy Bresler and Philippe Rigollet. He received his undergraduate degree in mathematics from Princeton University, where he was advised by Emmanuel Abbe. His interests are learning theory, average-case complexity, high-dimensional statistics, optimal transport</div></div><div class="gmail_default"><br></div><div class="gmail_default"><br></div></div><span style="font-family:Arial,Helvetica,sans-serif">--</span><br style="font-family:Arial,Helvetica,sans-serif"><div dir="ltr" style="font-family:Arial,Helvetica,sans-serif"><div dir="ltr"><b><font color="#3d85c6">Brandie Jones </font></b><div><div><div><font color="#3d85c6"><b><i>Executive </i></b></font><b style="color:rgb(61,133,198)"><i>Administrative Assistant</i></b></div></div><div><font color="#3d85c6">Toyota Technological Institute</font></div><div><font color="#3d85c6">6045 S. Kenwood Avenue</font></div><div><font color="#3d85c6">Chicago, IL  60637</font></div></div><div><font color="#3d85c6"><a href="http://www.ttic.edu/" target="_blank">www.ttic.edu</a> </font></div><div><font color="#3d85c6"><div style="background-color:rgb(238,238,238)">Working Remotely on Tuesdays</div></font></div></div></div></div></div>