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SUMMARY:Paulo Tabuada (UCLA)
DTSTART:20220609T160000Z
DTEND:20220609T170000Z
DTSTAMP:20260423T003257Z
UID:MPML/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MPML/77/">De
 ep neural networks\, universal approximation\, and geometric control</a>\n
 by Paulo Tabuada (UCLA) as part of Mathematics\, Physics and Machine Learn
 ing (IST\, Lisbon)\n\n\nAbstract\nDeep neural networks have drastically ch
 anged the landscape of several engineering areas such as computer vision a
 nd natural language processing. Notwithstanding the widespread success of 
 deep networks in these\, and many other areas\, it is still not well under
 stood why deep neural networks work so well. In particular\, the question 
 of which functions can be learned by deep neural networks has remained una
 nswered.\nIn this talk we give an answer to this question for deep residua
 l neural networks\, a class of deep networks that can be interpreted as th
 e time discretization of nonlinear control systems. We will show that the 
 ability of these networks to memorize training data can be expressed throu
 gh the control theoretic notion of controllability which can be proved usi
 ng geometric control techniques. We then add an additional ingredient\, mo
 notonicity\, to conclude that deep residual networks can approximate\, to 
 arbitrary accuracy with respect to the uniform norm\, any continuous funct
 ion on a compact subset of n-dimensional Euclidean space by using at most 
 n+1 neurons per layer. We will conclude the talk by showing how these resu
 lts pave the way for the use of deep networks in the perception pipeline o
 f autonomous systems while providing formal (and probability free) guarant
 ees of stability and robustness.\n
LOCATION:https://researchseminars.org/talk/MPML/77/
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