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SUMMARY:Optimal Approximation with Sparsely Connected Deep Neural Networks
  - Gitta Kutyniok (Technische Universität Berlin)
DTSTART:20171030T145000Z
DTEND:20171030T154000Z
UID:TALK94018@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Despite the outstanding success of deep neural networks in rea
 l-world applications\, most of the related research is empirically driven 
 and a mathematical foundation is almost completely missing. One central ta
 sk of a neural network is to approximate a function\, which for instance e
 ncodes a classification task. In this talk\, we will be concerned with the
  question\, how well a function can be approximated by a neural network wi
 th sparse connectivity. Using methods from approximation theory and applie
 d harmonic analysis\, we will derive a fundamental lower bound on the spar
 sity of a neural network. By explicitly constructing neural networks based
  on certain representation systems\, so-called $\\alpha$-shearlets\, we wi
 ll then demonstrate that this lower bound can in fact be attained.  Finall
 y\, we present numerical experiments\, which surprisingly show that alread
 y the standard backpropagation algorithm generates deep neural networks ob
 eying those optimal approximation rates. This is joint work with H. B&ouml
 \;lcskei (ETH Zurich)\, P. Grohs (Uni Vienna)\, and P. Petersen (TU Berlin
 ).
LOCATION:Seminar Room 1\, Newton Institute
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