{"id":3252,"date":"2025-04-22T07:02:50","date_gmt":"2025-04-22T07:02:50","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/04\/22\/2504-14425\/"},"modified":"2025-04-22T07:02:50","modified_gmt":"2025-04-22T07:02:50","slug":"2504-14425","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/04\/22\/2504-14425\/","title":{"rendered":"Optimal Scheduling of Dynamic Transport"},"content":{"rendered":"

Optimal Scheduling of Dynamic Transport
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arXiv:2504.14425v1 Announce Type: new
\nAbstract: Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this freedom. Though many popular methods seek straight line (i.e., zero acceleration) trajectories, we show here that a specific class of “curved” trajectories can significantly improve approximation and learning. In particular, we consider the unit-time interpolation of any given transport map $T$ and seek the schedule $tau: [0,1] to [0,1]$ that minimizes the spatial Lipschitz constant of the corresponding velocity field over all times $t in [0,1]$. This quantity is crucial as it allows for control of the approximation error when the velocity field is learned from data. We show that, for a broad class of source\/target measures and transport maps $T$, the emph{optimal schedule} can be computed in closed form, and that the resulting optimal Lipschitz constant is emph{exponentially smaller} than that induced by an identity schedule (corresponding to, for instance, the Wasserstein geodesic). Our proof technique relies on the calculus of variations and $Gamma$-convergence, allowing us to approximate the aforementioned degenerate objective by a family of smooth, tractable problems.<\/div>\n

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\n Panos Tsimpos, Zhi Ren, Jakob Zech, Youssef Marzouk
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Optimal Scheduling of Dynamic Transport arXiv:2504.14425v1 Announce Type: new Abstract: Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,2427,1172,112],"tags":[1486,15,2428],"class_list":["post-3252","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-ca","category-math-fa","category-stat-ml","tag-optimal","tag-time","tag-transport"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3252"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=3252"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3252\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=3252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=3252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=3252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}