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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Fundamental limits of deep generative neural netwo
rks - Helmut Bölcskei (ETH Zürich)
DTSTART;TZID=Europe/London:20211210T100000
DTEND;TZID=Europe/London:20211210T110000
UID:TALK165160AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165160
DESCRIPTION:Deep neural networks have been employed very succe
ssfully as generative models for complex natural d
ata such as images and natural\nlanguage. In pract
ice this is realized by training deep networks so
that they realize high-dimensional probability dis
tributions by transforming simple low-dimensional
distributions such as uniform or Gaussian. The aim
of this talk is to develop understanding of the f
undamental representational capabilities\nof deep
generative neural networks. Specifically\, \;w
e show that every d-dimensional probability distri
bution of bounded support can be generated through
deep ReLU networks out of a 1-dimensional uniform
input distribution. What is more\, this is possib
le without incurring a cost&mdash\;in terms of app
roximation error as measured in Wasserstein-distan
ce&mdash\;relative to generating the d-dimensional
target distribution from d independent random var
iables. This is enabled by a space-filling approac
h which elicits the importance of network depth in
driving the Wasserstein distance between the targ
et distribution and its neural network approximati
on to zero. Finally\, we show that \;\nthe num
ber of bits needed to encode the corresponding gen
erative networks equals the fundamental limit for
encoding probability distributions as dictated by
quantization theory.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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