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SUMMARY:Trainability and accuracy of artificial neural networks
DTSTART:20190522T171500
DTEND:20190522T183000
DTSTAMP:20260925T073458Z
UID:c020fdab239ab45a9197bbf163e62bd372ccb0625a3966db74a1de2f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Eric Vanden-Eijden\, New York University\n\nThe methods 
 and models of machine learning (ML) are rapidly becoming de facto tools fo
 r the analysis and interpretation of large data sets. Complex classificati
 on tasks such as speech and image recognition\, automatic translation\, de
 cision making\, etc. that were out of reach a decade ago are now routinely
  performed by computers with a high degree of reliability using (deep) neu
 ral networks. These performances suggest that it may be possible to repres
 ent high-dimensional functions with controllably small errors\, potentiall
 y outperforming standard interpolation methods based e.g. on Galerkin trun
 cation or finite elements. In support of this prospect\, in this talk I wi
 ll present results about the trainability and accuracy of neural networks\
 , obtained by mapping the parameters of the network to a system of interac
 ting particles relaxing on a potential determined by the loss function. Un
 like the particles themselves\, their empirical distribution evolves on a 
 convex landscape. This observation can be used to prove a dynamical varian
 t of the universal approximation theorem showing that the optimal neural n
 etwork representation can be attained by (stochastic) gradient descent\, w
 ith a approximation error scaling as the inverse of the network size. I wi
 ll also show how these findings can be used to accelerate the training of 
 networks and optimize their architecture\, using e.g nonlocal transport in
 volving birth/death processes in parameter space.\n 
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 &tree_groups=centres_nevralgiques%2Cacces%2Cmobilite_reduite%2Censeignemen
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STATUS:CONFIRMED
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