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UID:0-823@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20220517T110000
DTEND;TZID=Europe/Paris:20220517T120000
DTSTAMP:20220502T115122Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-pietro-rotondo-infn-milano/
SUMMARY:Séminaire du LPTMS : Pietro Rotondo (Infn Milano) - Salle des sém
 inaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 17 Mai 22 11:00
DESCRIPTION:Universal mean field upper bound for the generalisation gap of 
 deep neural networks\n Pietro Rotondo (Infn Milano)\n\nHybrid seminar: ons
 ite + zoom.\n\nhttps://cnrs.zoom.us/j/92485497120?pwd=c0dBZVkxT2xmUzNNZDhZ
 bU9lM2dsQT09\nMeeting ID: 924 8549 7120\nPasscode: dSQ0B2\n\n\nModern deep
  neural networks (DNNs) represent a formidable challenge for theorists: ac
 cording to the commonly accepted probabilistic framework that describes th
 eir performance\, these architectures should overfit due to the huge numbe
 r of parameters to train\, but in practice they do not. Here we employ res
 ults from replica mean field theory to compute the generalisation gap of m
 achine learning models with quenched features\, in the teacher-student sce
 nario and for regression problems with quadratic loss function. Notably\, 
 this framework includes the case of DNNs where the last layer is optimised
  given a specific realisation of the remaining weights. We show how these 
 results – combined with ideas from statistical learning theory – provi
 de a stringent asymptotic upper bound on the generalisation gap of fully t
 rained DNN as a function of the size of the dataset P. In particular\, in 
 the limit of large P and Nout (where Nout is the size of the last layer) a
 nd Nout ≪ P \, the generalisation gap approaches zero faster than 2Nout/
 P\, for any choice of both architecture and teacher function. Notably\, th
 is result greatly improves existing bounds from statistical learning theor
 y. We test our predictions on a broad range of architectures\, from toy fu
 lly-connected neural networks with few hidden layers to state-of-the-art d
 eep convolutional neural networks.\n
CATEGORIES:seminars
LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53
 0\, rue André Riviere\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\
 , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST 
 et du LPTMS\, bâtiment Pascal n°530:geo:0,0
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