<div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr"><div><div style="color:rgb(80,0,80)"><b style="font-family:arial,sans-serif">When:</b><span style="font-family:arial,sans-serif">          </span><b style="font-family:arial,sans-serif"> Friday, February 25th at <span style="background-color:rgb(255,255,0)">10:30am</span></b></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="#500050" style="font-family:arial,sans-serif"> </font><br><b style="font-family:arial,sans-serif;color:rgb(80,0,80)">Where:</b><b style="font-family:arial,sans-serif;color:rgb(80,0,80)">  </b><font color="#500050" style="font-family:arial,sans-serif">       Talk will be given </font><font color="#0000ff" face="arial, sans-serif" style="font-weight:bold"><u>live, in-person</u></font><font color="#0000ff" face="verdana, sans-serif" style="font-weight:bold"> </font><font face="arial, sans-serif" color="#000000">at</font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif">                     TTIC, 6045 S. Kenwood Avenue</font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif">                      5th Floor, Room 530<b><span style="color:black">              </span></b>   </font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black">Virtually:</span></b><span style="color:black">      via zoom: </span><a href="https://uchicagogroup.zoom.us/meeting/register/tJIvduChqjMiHNTEa-QzLrhMT1KJWHxWHqUh" target="_blank"><b><span style="color:blue">register in advance here</span></b></a> </font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black">Who:</span></b><b><span style="color:black"> </span></b><span style="color:black">           Alexander Razborov </span></font></p><table border="0" cellspacing="0" cellpadding="0" width="0" style="color:rgb(80,0,80);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;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:black"><font face="arial, sans-serif"> </font></span></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="arial, sans-serif" style="color:rgb(80,0,80)"><b><span style="color:black">Title:</span></b><b><span style="color:black"> </span></b><span style="color:black">           </span></font>Small Depth Threshold Circuits</p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></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 color="#000000">Abstract</font></b><font color="#500050">:     </font><span style="color:rgb(34,34,34)">Among many restricted circuit models studied in the circuit complexity, </span><font color="#500050">constant</font><span style="color:rgb(34,34,34)"> depth threshold circuits are of particular relevance to</span></p>theoretical machine learning, and particularly to the deep learning. I<br>will try to give an admittedly incomplete and subjective survey of the<br>area. We will begin with outlying these connections to ML and review<br>several major results about the representability and the approximation<br>error in the continuous case. In the rest of the talk we will survey<br>what is known for the discrete (Boolean) case, sometimes with proof<br>sketches, and list major open problems in the area.<p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"> </font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span style="color:black"><font face="arial, sans-serif">*********************************************************************************************</font></span></b></p><p class="MsoNormal" style="margin:0in 0in 8pt;color:rgb(80,0,80);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><font face="arial, sans-serif">Presence at TTIC requires being fully vaccinated for COVID-19 or having a TTIC or UChicago-approved exemption. Masks are required in all common areas. Full visitor guidance 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;color:rgb(80,0,80);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><span style="color:black"><font face="arial, sans-serif">*********************************************************************************************</font></span></b></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><i><span style="color:black"><font face="arial, sans-serif">Research at TTIC Seminar Series</font></span></i></b></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:black"><font face="arial, sans-serif"> </font></span></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-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></p><br></div><div><br></div><div><br></div><br clear="all"><div><div dir="ltr"><div dir="ltr"><br></div></div></div><div><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">Faculty Administrative Support</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></div></div></div>
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