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UID:www.tcs.tifr.res.in/event/1265
DTSTAMP:20230914T125957Z
SUMMARY:Scaling limits of stochastic optimization algorithms over large gra
 phs
DESCRIPTION:Speaker: Raghav Somani (University of Washington)\n\nAbstract: 
 \nWasserstein gradient flows often arise from mean-field interactions amon
 g exchangeable particles. In many interesting applications however\, the "
 particles" are edge weights in a graph whose vertex labels are exchangeabl
 e but not the edges themselves. Motivated by such graph optimization probl
 ems we investigate the question of optimization of functions over this dif
 ferent class of symmetries. Popular applications include training of large
  computational graphs like (Deep) Neural Networks. This body of work shows
  that discrete stochastic optimization algorithms over finite graphs have 
 a well-defined analytical scaling limit as the size of the network grows t
 o infinity. The limiting space is that of graphons\, a notion introduced b
 y Lovász and Szegedy to describe limits of dense graph sequences. The lim
 iting curves are given by a novel notion of McKean-Vlasov equations on gra
 phons and a corresponding notion of propagation of chaos holds. In the asy
 mptotically zero-noise case\, the limit is a gradient flow on the metric s
 pace of graphons. This is an attempt to generalize the Wasserstein calculu
 s to higher-order exchangeable structures.\n
URL:https://www.tcs.tifr.res.in/web/events/1265
DTSTART;TZID=Asia/Kolkata:20230117T160000
DTEND;TZID=Asia/Kolkata:20230117T170000
LOCATION:A201
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