The canonical method in generative modeling is to separate mannequin becoming into two blocks: outline first easy methods to pattern noise (e.g. Gaussian) and select subsequent what to do with it (e.g. utilizing a single map or flows). We discover on this work another route that ties sampling and mapping. We discover inspiration in second measures, a consequence that states that for any measure \u03c1, there exists a singular convex potential u<\/i> such that \u03c1 = \u2207u<\/i>\u266fe^{–u<\/i><\/sup>. Whereas this does appear to tie successfully sampling (from log\u2013concave distribution e^{–u<\/i><\/sup>) and motion (pushing particles by \u2207u<\/i>), we observe on easy examples (e.g., Gaussians or 1D distributions) that this alternative is in poor health\u2013fitted to sensible duties. We examine another factorization, the place \u03c1 is factorized as \u2207w*<\/i>\u266fe^{–w<\/i><\/sup>, the place w*<\/i> is the convex conjugate of a convex potential w<\/i>. We name this method conjugate second measures, and present much more intuitive outcomes on these examples. As a result of \u2207w*<\/i> is the Monge map between the log\u2013concave distribution e^{–w<\/i><\/sup> and \u03c1, we depend on optimum transport solvers to suggest an algorithm to recuperate w<\/i> from samples of \u03c1, and parameterize w<\/i> as an enter\u2013convex neural community. We additionally deal with the frequent sampling state of affairs through which the density of \u03c1 is thought solely as much as a normalizing fixed, and suggest an algorithm to study w<\/i> on this setting.<\/p>\n}}}}

\n
\u2020 CREST\u2013ENSAE, Institut Polytechnique de Paris<\/li>\n<\/ul>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"
The canonical method in generative modeling is to separate mannequin becoming into two blocks: outline first easy methods to pattern noise (e.g. Gaussian) and select subsequent what to do with it (e.g. utilizing a single map or flows). We discover on this work another route that ties sampling and mapping. We discover inspiration in second […]<\/p>\n","protected":false},"author":2,"featured_media":9078,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[55],"tags":[6593,2443,615,447,3845,1875,860,2157,4339],"class_list":["post-9076","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-machine-learning","tag-conjugate","tag-convex","tag-generation","tag-map","tag-measures","tag-moment","tag-potential","tag-sample","tag-single"],"_links":{"self":[{"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/posts\/9076","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9076"}],"version-history":[{"count":1,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/posts\/9076\/revisions"}],"predecessor-version":[{"id":9077,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/posts\/9076\/revisions\/9077"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=\/wp\/v2\/media\/9078"}],"wp:attachment":[{"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/techtrendfeed.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}