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SUMMARY:Feature Learning in Two-layer Neural Networks: The Effect of Data 
 Covariance - Murat A. Erdogdu (University of Toronto)
DTSTART:20240424T130000Z
DTEND:20240424T140000Z
UID:TALK213166@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:We study the effect of gradient-based optimization on feature 
 learning in two-layer neural networks. We consider a setting\nwhere the nu
 mber of samples is of the same order as the input\ndimension and show that
 \, when the input data is isotropic\, gradient descent always improves upo
 n the initial random features model in terms of prediction risk\, for a ce
 rtain class of targets. Further leveraging the practical observation that 
 data often contains additional structure\, i.e.\, the input covariance has
  non-trivial alignment with the target\, we prove that the class of learna
 ble targets can be significantly extended\, demonstrating a clear separati
 on between kernel methods and two-layer neural networks in this regime.\n
LOCATION:Centre for Mathematical Sciences\, MR14
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