Documents  68T99 | enregistrements trouvés : 8

- xi; 191 p.
ISBN 978-1-4704-1042-1

Contemporary mathematics , 0622

Localisation : Collection 1er étage

analyse multivariée # intelligence artificielle # big data # inférence non-paramétrique

68T99 ; 62H25 ; 62J07 ; 62F05 ; 62G05 ; 62M05 ; 62G08 ; 60-XX ; 62G99 ; 62H15 ; 62-06 ; 62-07 ; 62Gxx ; 62Hxx ; 00B25

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Research talks;Control Theory and Optimization;Mathematics in Science and Technology

We are interested in nonsmooth analysis of backpropagation as implemented in modern machine learning librairies, such as Tensorflow or Pytorch. First I will illustrate how blind application of
differential calculus to nonsmooth objects can be problematic, requiring a proper mathematical model.
Then I will introduce a weak notion of generalized derivative, named conservativity, and illustrate how it complies with calculus and optimization for well structured objects. We provide stability results for empirical risk minimization similar as in the smooth setting for the combination of nonsmooth automatic differentiation, minibatch stochastic approximation and first order optimization. This is joint work with Jérôme Bolte. We are interested in nonsmooth analysis of backpropagation as implemented in modern machine learning librairies, such as Tensorflow or Pytorch. First I will illustrate how blind application of
differential calculus to nonsmooth objects can be problematic, requiring a proper mathematical model.
Then I will introduce a weak notion of generalized derivative, named conservativity, and illustrate how it complies with calculus and optimization for ...

65K05 ; 65K10 ; 68T99

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Research talks;Computer Science;Control Theory and Optimization;Probability and Statistics

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training and generalization behavior of infinitely wide two-layer neural networks with homogeneous activations. We show that the limits of the gradient flow on exponentially tailed losses can be fully characterized as a max-margin classifier in a certain non-Hilbertian space of functions. Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training and generalization behavior of infinitely wide two-layer neural networks with homogeneous activations. We show that the limits of the gradient flow on exponentially tailed losses can be fully characterized as a ...

65K10 ; 65K05 ; 68W99 ; 68T99

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- 160 p.
ISBN 978-0-8176-3332-5

Progress in computer science , 0007

Localisation : Ouvrage RdC (DONN)

locomotion # processus de données temps réel # robotique

68T99 ; 68Txx

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- 466 p.
ISBN 978-0-19-851973-7

Localisation : Ouvrage RdC (PENR)

axiomatique # biomathématique # épistémologie des mathématiques # gravitation # informatique # intelligence artificielle # philosophie # philosophie des mathématiques # psychologie # relativité # théorie quantique

00A69 ; 68T99 ; 81P99 ; 83C45 ; 92J99

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- 218 p.
ISBN 978-2-225-80471-7

Etudes et recherches en informatique

Localisation : Ouvrage RdC (WERT)

68T99

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- 63 p.
ISBN 978-2-86601-153-6

Technologies de pointe

Localisation : Ouvrage RdC (POME)

système expert # moteur d'inférence # contrôle # chaînage # représentation des connaissances

68T99 ; 68-01

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