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SUMMARY:Compositional Features and Feedforward Neural Networks for High Di
 mensional Problems - Wei  Kang (Naval Postgraduate School)
DTSTART:20211116T163000Z
DTEND:20211116T170000Z
UID:TALK165418@talks.cam.ac.uk
DESCRIPTION:Deep learning has had many impressive empirical successes in s
 cience and industries. On the other hand\, the lack of theoretical underst
 anding of the field has been a large barrier to the adoption of the techno
 logy. In this talk\, I will discuss some compositional features of high di
 mensional problems and their mathematical properties that shed light on th
 e question why deep learning works for high dimensional problems. It is wi
 dely observed in science and engineering that complicated and high dimensi
 onal information input-output relations can be represented as compositions
  of functions with low input dimensions. Their compositional structures ca
 n be effectively represented using layered directed acyclic graphs (layere
 d DAGs). Based on the layered DAG formulation\, an algebraic framework and
  approximation theory are developed for compositional functions including 
 neural networks. The theory leads to the proof of several complexity/appro
 ximation error bounds of deep neural networks for problems of regression a
 nd dynamical systems.
LOCATION:Seminar Room 1\, Newton Institute
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