{"id":185,"date":"2023-11-13T12:24:55","date_gmt":"2023-11-13T11:24:55","guid":{"rendered":"https:\/\/pole-acs.lis-lab.fr\/?p=185"},"modified":"2023-11-13T12:24:55","modified_gmt":"2023-11-13T11:24:55","slug":"alessandro-scagliotti","status":"publish","type":"post","link":"https:\/\/pole-acs.lis-lab.fr\/?p=185","title":{"rendered":"Alessandro Scagliotti"},"content":{"rendered":"<p><strong>TUM Munich<\/strong><\/p>\n<p >30 novembre 2023, 14.00<br \/>\nSalle X133<br \/>\nCampus Toulon<\/p>\n<h2><strong>Ensemble optimal control: ResNets, diffeomorphisms approximation and<br \/>\nNormalizing Flows<br \/>\n<\/strong><\/h2>\n<p>In the last years it was observed that Residual Neural<br \/>\nNetworks (ResNets) can be interpreted as discretizations of control<br \/>\nsystems, bridging ResNets (and, more generally, Deep Learning) with<br \/>\nControl Theory. In the first part of this seminar we formulate the task<br \/>\nof a data-driven reconstruction of a diffeomorphism as an ensemble<br \/>\noptimal control problem. In the second part we adapt this machinery to<br \/>\naddress the problem of Normalizing Flows: after observing some samplings<br \/>\nof an unknown probability measure, we want to (approximately) construct<br \/>\na transport map that brings a \u201csimple\u201d distribution (e.g., a Gaussian)<br \/>\nonto the unknown target distribution. In both the problems we use tools<br \/>\nfrom $\\Gamma$-convergence to study the limiting case when the size of<br \/>\nthe data-set tends to infinity. <\/br><\/p>\n<p>This talk is based on the papers <\/br><\/p>\n<p><a href=\"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/mcrf.2022036\"><i>Deep Learning approximation of diffeomorphisms via linear-control systems.<\/i><\/a><\/br><br \/>\n<a href=\"http:\/\/export.arxiv.org\/abs\/2311.01404\"> <i> Normalizing flows as approximations of optimal transport maps via<br \/>\nlinear-control neural ODEs<\/i><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>TUM Munich 30 novembre 2023, 14.00 Salle X133 Campus Toulon Ensemble optimal control: ResNets, diffeomorphisms approximation and Normalizing Flows In the last years it was observed that Residual Neural Networks (ResNets) can be interpreted as discretizations of control systems, bridging ResNets (and, more generally, Deep Learning) with Control Theory. In the first part of this &hellip; <a href=\"https:\/\/pole-acs.lis-lab.fr\/?p=185\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Alessandro Scagliotti<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,7],"tags":[],"class_list":["post-185","post","type-post","status-publish","format-standard","hentry","category-13","category-toulon"],"_links":{"self":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=185"}],"version-history":[{"count":2,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/185\/revisions"}],"predecessor-version":[{"id":187,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=\/wp\/v2\/posts\/185\/revisions\/187"}],"wp:attachment":[{"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pole-acs.lis-lab.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}