<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ligatures:standardcontextual;}
h1
{mso-style-priority:9;
mso-style-link:"Heading 1 Char";
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:24.0pt;
font-family:"Calibri",sans-serif;
font-weight:bold;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
span.Heading1Char
{mso-style-name:"Heading 1 Char";
mso-style-priority:9;
mso-style-link:"Heading 1";
font-family:"Calibri",sans-serif;
mso-ligatures:none;
font-weight:bold;}
span.odd
{mso-style-name:odd;}
span.date-display-single
{mso-style-name:date-display-single;}
span.date-display-range
{mso-style-name:date-display-range;}
span.date-display-start
{mso-style-name:date-display-start;}
span.date-display-end
{mso-style-name:date-display-end;}
span.fn
{mso-style-name:fn;}
span.map-icon
{mso-style-name:map-icon;}
span.locality
{mso-style-name:locality;}
span.region
{mso-style-name:region;}
span.postal-code
{mso-style-name:postal-code;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;
mso-ligatures:none;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1027" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><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;mso-ligatures:none;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01DA4482.2CFEBC20" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black;mso-ligatures:none'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;color:#286DC0'>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><h1 style='mso-margin-top-alt:.1in;margin-right:0in;margin-bottom:0in;margin-left:0in;background:white'><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#222222'>Mikhail Belkin, <span class=odd>University of California San Diego</span></span><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#222222;font-weight:normal'><o:p></o:p></span></h1><p class=MsoNormal style='background:white'><!--[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">
<v:stroke joinstyle="miter" />
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0" />
<v:f eqn="sum @0 1 0" />
<v:f eqn="sum 0 0 @1" />
<v:f eqn="prod @2 1 2" />
<v:f eqn="prod @3 21600 pixelWidth" />
<v:f eqn="prod @3 21600 pixelHeight" />
<v:f eqn="sum @0 0 1" />
<v:f eqn="prod @6 1 2" />
<v:f eqn="prod @7 21600 pixelWidth" />
<v:f eqn="sum @8 21600 0" />
<v:f eqn="prod @7 21600 pixelHeight" />
<v:f eqn="sum @10 21600 0" />
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect" />
<o:lock v:ext="edit" aspectratio="t" />
</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;margin-left:0;margin-top:0;width:120.85pt;height:145pt;z-index:251659264;visibility:visible;mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;mso-position-horizontal-relative:text;mso-position-vertical:absolute;mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
<v:imagedata src="cid:image002.jpg@01DA4482.2CFEBC20" o:title="" />
<w:wrap type="square"/>
</v:shape><![endif]--><![if !vml]><img width=161 height=193 style='width:1.677in;height:2.0104in' src="cid:image003.jpg@01DA4D1C.A36C2E90" align=left hspace=12 v:shapes="Picture_x0020_1"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Date:</span></b></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> Monday, January 22, 2024</span><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Time</span><span style='color:black'>:</span></b></span><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> 4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>5:00PM</span></span><o:p></o:p></p><p class=MsoNormal style='background:white'><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Location</span><span style='color:black'>:</span></b></span><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'> Kline Tower</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'> <span class=map-icon><span style='letter-spacing:.6pt'><a href="http://maps.google.com/?q=219+Prospect+Street%2C+13+Floor%2C+Rm+1327%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:#286DC0'>see map</span></a> </span></span><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>219 Prospect Street, 13 Floor, Rm 1327<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Zoom</span></b></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'> </span><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Link</span><span style='color:black'>:</span></b></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'> <a href="https://yale.zoom.us/j/94223816617">https://yale.zoom.us/j/94223816617</a> Meeting ID: 942 2381 6617<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><a href="http://misha.belkin-wang.org/"><span style='color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Title: <b>Toward a practical theory of deep learning<o:p></o:p></b></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Information and Abstract: <o:p></o:p></span></b></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Remarkable recent advances in deep neural networks are rapidly changing science and society.<br>Never before had a technology been deployed so widely and so quickly with so little understanding of its fundamentals. I will argue that developing a fundamental mathematical theory of deep learning is necessary for a successful AI transition and, furthermore, that such a theory may well be within reach. I will discuss what a theory might look like and some of its ingredients that we already have available.<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>In particular, I will discuss how deep neural neural networks of various architectures learn features and how the lessons of deep learning can be incorporated in non-backpropagation-based algorithms that we call Recursive Feature Machines. I will provide a number of experimental results on different types of data, including texts and images, as well as some connections to classical statistical methods, such as Iteratively Reweighted Least Squares. <br> <o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>3:30pm - Pre-talk meet and greet teatime – Kline Tower, 219 Prospect Street, 13 floor, there will be light snacks and beverages in the kitchen area.</span></strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p></o:p></span></p><p class=MsoNormal><b><i><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></i></b></p><p class=MsoNormal><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 <a href="http://statistics.yale.edu/"><span style='color:black'>http://statistics.yale.edu/</span></a></span><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-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<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'>t 203.432.0666<br>f 203.432.0633</span><o:p></o:p></p></div></body></html>