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SUMMARY:Lénaic Chizat : "Quantitative Convergence of Kernelized Wasserste
 in Gradient Flows"
DTSTART:20260512T120000Z
DTEND:20260512T130000Z
DTSTAMP:20260714T133100Z
UID:indico-event-15846@indico.math.cnrs.fr
DESCRIPTION: \n\nAbstract:\nSeveral machine-learning algorithms can be de
 scribed\, in the mean-field limit\, as transport/continuity PDEs whose vel
 ocity field is regularized by a smoothing kernel. This is the case for Was
 serstein gradient flows of Kernel Mean Discrepancies (KMD)\, which arise i
 n the large-width limit of shallow neural-network training\, and for Stein
  Variational Gradient Flow (SVGF)\, a sampling method based on interacting
  particles.\nUnderstanding the performance of these algorithms therefore l
 eads to questions about the long-time behavior of nonlocal PDEs. I will pr
 esent an approach to quantitative local convergence for these flows\, that
  yields sharp polynomial rates for Riesz-type kernels. The key difficulty 
 is that the energy dissipation controls a weaker norm than the energy. The
  proof compensates for this loss through Sobolev interpolation and propaga
 tion of regularity.\n\n\nThis is joint work with Maria Colombo\, Roberto C
 olombo and Xavier Fernández-Real\n\n\nhttps://indico.math.cnrs.fr/event/1
 5846/
URL:https://indico.math.cnrs.fr/event/15846/
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