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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#467886" vlink="#96607D" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01DB7631.54C05ED0" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black;mso-ligatures:none'> </span><span style='font-size:12.0pt;color:black'><a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:14.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Shuangping Li, Stanford University<o:p></o:p></span></b></p><p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=128 height=153 style='width:1.3333in;height:1.5937in' src="cid:image003.jpg@01DB7631.CAB97B30" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Date: Monday, February 10, 2025<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Time: 12:00PM to 1:00PM<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Location: Kline Tower, 13th Floor, Rm. 1327 <a href="http://maps.google.com/?q=219+Prospect+Street%2C+New+Haven%2C+CT%2C+06511%2C+us">See map</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>219 Prospect Street<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>and via Webcast: <a href="https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=0d95c606-a684-4393-ae0c-b2640126583b">https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=0d95c606-a684-4393-ae0c-b2640126583b</a><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Title: Phase Transitions and Algorithmic Aspects of the Binary Perceptron<o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Information and Abstract: The binary perceptron model, a simple single-layer neural network, has a rich history in theoretical physics and machine learning. This model considers the problem of finding a sign vector that satisfies a set of random halfspace constraints. The two central questions are: for what constraint densities do solutions exist with high probability, and can we efficiently find a solution when one exists?<br> <br>In this talk, I will discuss my work addressing both questions, guided by long-standing conjectures from physics. These conjectures predict a sharp satisfiability threshold for the existence of solutions, and a strong freezing property (where almost all solutions are isolated, suggesting that finding solutions using polynomial-time algorithms is typically hard). For the symmetric binary perceptron, we rigorously establish both predictions. Furthermore, the strong freezing property is particularly intriguing, because empirical evidence shows that polynomial time algorithms often succeed in finding a solution, challenging the typically hard prediction. This suggests that such algorithms find atypical solutions. We establish formally this phenomenon, showing that at low constraint density, there exists a rare but well-connected cluster of solutions, and that an efficient multiscale majority algorithm can find solutions in such a cluster with high probability. Additionally, we modify the canonical discrepancy minimization algorithms to solve the binary perceptron problem. We analyze the performance of our algorithm, yielding new algorithmic results.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Speaker bio: Shuangping Li is a Stein Fellow in statistics at Stanford University. She earned her PhD in applied and computational mathematics from Princeton University under the guidance of Professors Allan Sly and Emmanuel Abbe. Her research lies at the intersection of probability theory, theory of algorithms and complexity, high dimensional statistics, and theoretical machine learning.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Lunch at 11:30am in room 1307<br>Talk at 12:00-1:00pm in room 1327A<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><a href="https://www.facebook.com/YaleUniversity"><br></a></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>For more details and upcoming events visit our website at </span><span style='font-size:12.0pt'><a href="https://statistics.yale.edu/calendar"><span style='font-family:"Arial",sans-serif;color:#467886;mso-ligatures:none'>https://statistics.yale.edu/calendar</span></a></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>. </span><span style='font-size:12.0pt;mso-ligatures:none'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Department of Statistics and Data Science<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>Yale University<br>Kline Tower<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>219 Prospect Street<br>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><a href="https://statistics.yale.edu/"><span style='color:#467886'>https://statistics.yale.edu/</span></a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>