{"id":111,"date":"2020-08-14T12:14:55","date_gmt":"2020-08-14T16:14:55","guid":{"rendered":"http:\/\/eventos.cmm.uchile.cl\/probseminar\/?p=111"},"modified":"2020-09-17T16:17:43","modified_gmt":"2020-09-17T19:17:43","slug":"a-mean-field-theory-for-certain-deep-neural-networks","status":"publish","type":"post","link":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/2020\/08\/a-mean-field-theory-for-certain-deep-neural-networks\/","title":{"rendered":"A mean-field theory for certain deep neural networks"},"content":{"rendered":"<h3>Speaker: Roberto Imbuzeiro Oliveira<br \/>\nIMPA<\/h3>\n<h3>Date: Aug 20, 2020 at 15:00<\/h3>\n<p><strong>Abstract:<\/strong> A natural approach to understand overparameterized deep neural networks is to ask if there is some kind of natural limiting behavior when the number of neurons diverges. We present a rigorous limit result of this kind for networks with complete connections and &#8220;random-feature-style&#8221; first and last layers. Specifically, we show that network weights are approximated by certain &#8220;ideal particles&#8221; whose distribution and dependencies are described by McKean-Vlasov mean-field model. We will present the intuition behind our approach; sketch some of the key technical challenges along the way; and connect our results to some of the recent literature on the topic.<\/p>\n<p><strong>Venue:<\/strong> Online via Zoom (if you are interested in the link please send a message to the organizers through the contact form)<\/p>\n<p><a href=\"https:\/\/drive.google.com\/file\/d\/1UgPAa4coYiyP9FjO9SqJUI_S6HE1yPGw\/view?usp=sharing\">Video<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Roberto Imbuzeiro Oliveira<br \/>\nIMPA<\/p>\n","protected":false},"author":25,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[4,3],"tags":[],"class_list":["post-111","post","type-post","status-publish","format-standard","hentry","category-past-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/posts\/111","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/comments?post=111"}],"version-history":[{"count":9,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/posts\/111\/revisions"}],"predecessor-version":[{"id":125,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/posts\/111\/revisions\/125"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/media?parent=111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/categories?post=111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/probseminar\/wp-json\/wp\/v2\/tags?post=111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}