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"><span style='font-size:22.0pt;font-family:"Lucida Sans",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@01D90A24.1D6F15A0" alt="Department of Statistics and Data Science
"></span></a> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal><b><i><span style='font-size:14.0pt'>In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220, with an option of remote participation via zoom.<o:p></o:p></span></i></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet, DL Suite 222, Room 228<o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:15.0pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt'><a href="https://statistics.yale.edu/seminars/joan-bruna-1"><span style='color:windowtext;text-decoration:none'>Joan Bruna</span></a>, New York University<o:p></o:p></span></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=135 height=160 style='width:1.4062in;height:1.6666in' src="cid:image003.jpg@01D90E05.09D4D9F0" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#003C76'><o:p></o:p></span></span></p><p class=MsoNormal><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Date</span></b></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>: Monday, December 12, 2022<o:p></o:p></span></span></p><p class=MsoNormal><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Time</span></b></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>: </span></span><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>5:00PM</span></span><o:p></o:p></p><p class=MsoNormal><span class=date-display-single><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Location</span></b></span><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>: Dunbar Lab. </span></span><span class=map-icon><span style='font-size:12.0pt;font-family:"Arial",sans-serif;letter-spacing:.6pt'><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Rm.+220%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:#286DC0'>see map</span></a> </span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>10 Hillhouse Avenue, Rm. 220<o:p></o:p></span></p><p class=MsoNormal><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://statistics.yale.edu/seminars/joan-bruna-1">https://statistics.yale.edu/seminars/joan-bruna-1</a><o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Zoom Option:</span></b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> / Password: 24</span><o:p></o:p></p><p class=MsoNormal><b><o:p> </o:p></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:15.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>Title: On Symmetries and Feature Learning in Simple Neural Networks<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>Information and Abstract: <o:p></o:p></span></b></p><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>For all their mathematical mysteries, two important features of neural networks are their ability to encode symmetries into their architectures, and their ability to ‘discover’ hidden low-dimensional structures within high-dimensional data. In this talk, I will cover two snippets capturing each of these phenomena. In the first part, we will study approximation properties of symmetric and antisymmetric functions by neural networks, and establish an exponential advantage of pairwise models (underpinning transformers) over unary ones (underpinning ‘DeepSets’). In the second part, we study the learnability of ‘single-index models’, a class of semiparametric models with hidden low-dimensional structure, and show how shallow neural networks are able to learn them with near optimal sample complexity, showcasing the benefits of feature learning in the high-dimensional regime. <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>Joint work with A. Zweig (first part) and A. Bietti, MJ Song and C. Sanford (second part). <o:p></o:p></span></p><p class=MsoNormal><em><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220, with an option of remote participation via zoom.</span></b></em><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Link: </span></strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Password: 24<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Or Telephone</span><span lang=JA style='font-size:12.0pt;font-family:"MS Gothic"'>：</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Meeting ID: 924 1107 7917<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><o:p> </o:p></p><h2 style='margin:0in;box-sizing: inherit;font-feature-settings: "kern", "liga", "dlig"'><span style='font-family:"Georgia",serif;font-weight:normal'>Department of Statistics and Data Science<o:p></o:p></span></h2><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>