BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicolas Papadakis (University of Bordeaux) DTSTART:20210608T101500Z DTEND:20210608T114500Z DTSTAMP:20260423T022603Z UID:MathDeep/8 DESCRIPTION:Title: On the learning of Wasserstein generative models\nby Nicolas Papadaki s (University of Bordeaux) as part of Mathematics of Deep Learning\n\n\nAb stract\nThe problem of WGAN (Wasserstein Generative Adversarial Network) l earning is an instance of optimization problems where one wishes to find\, among a parametric class of distributions\, the one which is closest to a target distribution in terms of an optimal transport (OT) distance. Apply ing a gradient-based algorithm for this problem requires to express the gr adient of the OT distance with respect to one of its argument\, which can be related to the solutions of the dual problem (Kantorovich potentials). The first part of this talk aims at finding conditions that ensure the exi stence of such gradient. After discussing regularity issues that may appea r with discrete target measures\, we will show that regularity problems ar e avoided when using entropy-regularized OT and/or considering the semi-di screte formulation of OT. Then\, we will see how these gradients can be ex ploited in a stable way to address some imaging problems where the target discrete measure is reasonably large. Using OT distances between multi-sca le patch distributions\, this allows to estimate a generative convolutiona l network that can synthesize an exemplar texture in a faithful and effici ent way.\nThis is a joint work with Antoine Houdard\, Arthue Leclaire and Julien Rabin.\n LOCATION:https://researchseminars.org/talk/MathDeep/8/ END:VEVENT END:VCALENDAR