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SUMMARY:Regularized linear autoencoders\, the Morse theory of loss\, and b
 ackprop in the brain - Jon Bloom (Broad Institute of MIT and Harvard)
DTSTART:20190624T130000Z
DTEND:20190624T140000Z
UID:TALK124222@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:When trained to minimize the distance between the data and its
  reconstruction\, linear autoencoders (LAEs) learn the subspace spanned by
  the top principal directions but cannot learn the principal directions th
 emselves. We prove that L2-regularized LAEs are symmetric at all critical 
 points and learn the principal directions as the left singular vectors of 
 the decoder. We smoothly parameterize the critical manifold and relate the
  minima to the MAP estimate of probabilistic PCA. Finally\, we consider im
 plications for PCA algorithms\, computational neuroscience\, and the algeb
 raic topology of deep learning. \n\nICML 2019.
LOCATION:MR12
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