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SUMMARY:Deep Learning in High Dimension: Neural Network Approximation of A
 nalytic Maps of Gaussians. - Christoph Schwab (ETH Zürich)
DTSTART:20211201T170000Z
DTEND:20211201T183000Z
UID:TALK166498@talks.cam.ac.uk
DESCRIPTION:For artificial deep neural networks with ReLU activation\,we p
 rove new expression rate bounds forparametric\, analytic functions whereth
 e parameter dimension could be infinite.Approximation rates are in mean sq
 uare on the unboundedparameter range with respect to product gaussian meas
 ure.Approximation rate bounds are free from the CoD\, anddetermined by sum
 mability of Wiener-Hermite PC expansion coefficients.Sufficient conditions
  for summability are quantified holomorphyon products of strips in the com
 plex domain.Applications comprise DNN expression rate bounds of deep-NNsfo
 r response surfaces of elliptic PDEs with log-gaussianrandom field inputs\
 , and for the posterior densities of thecorresponding Bayesian inverse pro
 blems.Variants of proofs which are constructive are outlined.(joint work w
 ith Jakob Zech\, University of Heidelberg\, Germany\,&nbsp\;and with Dinh 
 Dung and Nguyen Van Kien\, Hanoi\, Vietnam)References:https://math.ethz.ch
 /sam/research/reports.html?id=982
LOCATION:Seminar Room 2\, Newton Institute
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