<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">Bom dia a todos,<div><br></div><div>O Roberto é um pesquisador que navega fluentemente na probabilidade, estatística e machine learning em seus níveis mais fundamentais. Certamente será uma apresentação muito oportuna pra nosso Centro de Estatística, Ciência de Dados e Decisao , do Insper. </div><div><br></div><div>Todos são muito bem vindos.</div><div><br></div><div>Abs,</div><div>Hedibert </div><br><div dir="ltr">Sent from Hedibert's iPhone</div><div dir="ltr"><br>Begin forwarded message:<br><br></div><blockquote type="cite"><div dir="ltr"><b>From:</b> Hedibert Freitas Lopes <HedibertFL@insper.edu.br><br><b>Date:</b> October 10, 2019 at 9:05:36 AM GMT-3<br><b>To:</b> Hedibert Lopes <hedibert@gmail.com><br><b>Subject:</b> <b>Fwd: Lembrete: Seminário Acadêmico de Ciência de Dados e Decisão com Roberto Imbuzeiro do Instituto de Matemática Pura e Aplicada - IMPA</b><br><br></div></blockquote><blockquote type="cite"><div dir="ltr"> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <br> <br> <div dir="ltr">Sent from Hedibert's iPhone</div> <div dir="ltr"><br> Begin forwarded message:<br> <br> </div> <blockquote type="cite"> <div dir="ltr"><b>From:</b> Insper - Seminários Acadêmicos <seminariosacademicos@insper.edu.br><br> <b>Date:</b> October 10, 2019 at 9:01:26 AM GMT-3<br> <b>Subject:</b> <b>Lembrete: Seminário Acadêmico de Ciência de Dados e Decisão com Roberto Imbuzeiro do Instituto de Matemática Pura e Aplicada - IMPA</b><br> <br> </div> </blockquote> <blockquote type="cite"> <div dir="ltr"> <meta name="Generator" content="Microsoft Word 15 (filtered medium)">  <style></style>  <div class="WordSection1"> <p class="MsoNormal"><o:p> </o:p></p> <div align="center"> <table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" width="0" style="width:450.0pt"> <tbody> <tr> <td valign="top" style="padding:0cm 0cm 0cm 0cm"> <p class="MsoNormal"><img width="599" height="181" style="width:6.2395in;height:1.8854in" id="Imagem_x0020_1" alt="cid:image001.png@01D4C861.DA6A4ED0" src="cid:image001.png@01D55E79.461FCA80"><span style="mso-fareast-language:EN-US"><o:p></o:p></span></p> </td> </tr> </tbody> </table> </div> <p class="MsoNormal"><span style="display:none"><o:p> </o:p></span></p> <div align="center"> <table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" width="0" style="width:450.0pt"> <tbody> <tr> <td style="background:white;padding:30.0pt 37.5pt 37.5pt 37.5pt"> <p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-line-height-alt:19.5pt"> <b><span style="font-size:24.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US">Ciência de Dados e Decisão</span></b><b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US"><br> </span></b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US">Seminários Acadêmicos</span><span style="mso-fareast-language:EN-US"><o:p></o:p></span></p> <p class="MsoNormal"><b><span lang="EN-US" style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Mean-field models for deep neural networks<o:p></o:p></span></b></p> <p class="MsoNormal"><b><span lang="EN-US" style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"><o:p> </o:p></span></b></p> <p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Palestrante:</span></b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"> Roberto Imbuzeiro</span><span style="mso-fareast-language:EN-US"><o:p></o:p></span></p> <p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Universidade:</span></b> <span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"> Instituto de Matemática Pura e Aplicada – IMPA<o:p></o:p></span></p> <p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align:justify"><span lang="EN-US" style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Deep neural networks (DNN) are behind many of the recent advances in artificial intelligence and pattern recognition, from natural language processing to image labelling. However, we lack a good theoretical understanding of what makes DNNs work. It is not even understood why "overparameterization" -- ie. adding more and more neurons to a network -- allows for better performance, even though it presumably increases the risk of overfitting.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align:justify"><span lang="EN-US" style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Ths talk will present a potential approach to understanding DNNs with a very large number of parameters. In a nutshell, we show that certain overparameterized DNNs may be approximated by a new class of mean-field models that are amendable to further analysis. This partially generalizes previous results on shallow neural nets by several different authors. In particular, our result suggests that overparameterization has a kind of regularizing effect on the network. Our mean-field model is related to mean-field games and many other classes of models from several areas that carry the "mean-field" or "McKean-Vlasov" prefix. Still, we will not assume any previous familiarity with the topic of mean-field systems. <br> Joint work with Dyego Araújo and Daniel Yukimura from IMPA.<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-US" style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;line-height:19.5pt"> <b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US">Data:</span></b><span style="mso-fareast-language:EN-US"> </span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">11/10/2019<br> </span><b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US">Horário:</span></b><span style="mso-fareast-language:EN-US"> </span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">12h<br> </span><b><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#C00026;mso-fareast-language:EN-US">Local:</span></b><span style="mso-fareast-language:EN-US"> </span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US">Sala Paulo Renato de Souza - 2º andar- Insper </span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042"><img width="19" height="19" style="width:.1979in;height:.1979in" id="Imagem_x0020_2" alt="cid:image002.png@01D4C861.DA6A4ED0" src="cid:image002.png@01D55E79.461FCA80"></span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:#414042;mso-fareast-language:EN-US"> <br> Rua Quatá, 300 – Vila Olímpia, São Paulo/SP<br> Estacionamento: Rua Uberabinha, s/n</span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"><o:p></o:p></span></p> <p 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institucional.</span></i><span style="mso-fareast-language:EN-US"><o:p></o:p></span></p> </td> </tr> <tr> <td style="background:#C00026;padding:0cm 0cm 0cm 0cm"> <p class="MsoNormal"><span style="mso-fareast-language:EN-US"> <o:p></o:p></span></p> </td> </tr> </tbody> </table> </div> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><span style="color:#1F497D"><o:p> </o:p></span></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><o:p> </o:p></p> <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span 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