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UID:news841@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190319T144730
DTSTART;TZID=Europe/Zurich:20190403T110000
SUMMARY:Seminar in probability theory: Arthur Jacot (EPFL)
DESCRIPTION:We show that the behaviour of a Deep Neural Network (DNN) durin
 g gradient descent is described by a new kernel: the Neural Tangent Kernel
  (NTK). More precisely\, as the parameters are trained using gradient desc
 ent\, the network function (which maps the network inputs to the network o
 utputs) follows a so-called kernel gradient descent w.r.t. the NTK. We pro
 ve that as the network layers get wider and wider\, the NTK converges to a
  deterministic limit at initialization\, which stays constant during train
 ing. This implies in particular that if the NTK is positive definite\, the
  network function converges to a global minimum. The NTK also describes ho
 w DNNs generalise outside the training set: for a least squares cost\, the
  network function converges in expectation to the NTK kernel ridgeless reg
 ression\, explaining how DNNs generalise in the so-called overparametrized
  regime\, which is at the heart of most recent developments in deep learni
 ng.
X-ALT-DESC:We show that the behaviour of a Deep Neural Network (DNN) during
  gradient descent is described by a new kernel: the Neural Tangent Kernel 
 (NTK). More precisely\, as the parameters are trained using gradient desce
 nt\, the network function (which maps the network inputs to the network ou
 tputs) follows a so-called kernel gradient descent w.r.t. the NTK. We prov
 e that as the network layers get wider and wider\, the NTK converges to a 
 deterministic limit at initialization\, which stays constant during traini
 ng. This implies in particular that if the NTK is positive definite\, the 
 network function converges to a global minimum. The NTK also describes how
  DNNs generalise outside the training set: for a least squares cost\, the 
 network function converges in expectation to the NTK kernel ridgeless regr
 ession\, explaining how DNNs generalise in the so-called overparametrized 
 regime\, which is at the heart of most recent developments in deep learnin
 g. 
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