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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-aukosh-jagannath
SUMMARY:Tutte colloquium-Aukosh Jagannath
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:: The training dynamics and local geometry of
  high-dimensional\nlearning\n\nSPEAKER:\n Aukosh Jagannath\n\nAFFILIATION:
 \n University of À¶Ý®ÊÓƵ\n\nLOCATION:\n MC 5501\n\nABSTRACT:Many modern d
 ata science tasks can be expressed as optimizing\na complex\, random funct
 ions in high dimensions. The go-to methods for\nsuch problems are variatio
 ns of stochastic gradient descent (SGD)\,\nwhich perform remarkably well
 —c.f. the success of modern neural\nnetworks. However\, the rigorous ana
 lysis of SGD on natural\,\nhigh-dimensional statistical models is in its i
 nfancy. In this talk\,\nwe study a general model that captures a broad ran
 ge of learning\ntasks\, from Matrix and Tensor PCA to training two-layer n
 eural\nnetworks to classify mixture models. We show the evolution of natur
 al\nsummary statistics along training converge\, in the high-dimensional\n
 limit\, to a closed\, finite-dimensional dynamical system called their\nef
 fective dynamics. We then turn to understanding the landscape of\ntraining
  from the point-of-view of the algorithm. We show that in this\nlimit\, th
 e spectrum of the Hessian and Information matrices admit an\neffective spe
 ctral theory: the limiting empirical spectral measure and\noutliers have e
 xplicit characterizations that depend only on these\nsummary statistics. I
  will then illustrate how these techniques can be\nused to give rigorous d
 emonstrations of phenomena observed in the\nmachine learning literature su
 ch as the lottery ticket hypothesis and\nthe \"spectral alignment\" phenom
 enona. This talk surveys a series of\njoint works with G. Ben Arous (NYU)\
 , R. Gheissari (Northwestern)\, and\nJ. Huang (U Penn).\n\nThis talk is ba
 sed on joint work with Saeed Ghadimi and Henry\nWolkowicz from University 
 of À¶Ý®ÊÓƵ and Diego Cifuentes and Renato\nMonteiro from Georgia Tech.\n\
 n \n\n \n 
DTSTAMP:20250706T090426Z
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