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PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
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X-WR-CALNAME:Département de mathématiques et applications
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
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DTSTART:20210328T010000
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DTSTART;TZID=Europe/Paris:20211021T104500
DTEND;TZID=Europe/Paris:20211021T114500
DTSTAMP:20260407T103736
CREATED:20211109T150605Z
LAST-MODIFIED:20211109T150733Z
UID:14472-1634813100-1634816700@www.math.ens.psl.eu
SUMMARY:Machine learning and applied mathematics
DESCRIPTION:The recent success of machine learning suggests that neural networks may be capable of approximating high-dimensional functions with controllably small errors. As a result\, they could outperform standard function interpolation methods that have been the workhorses of scientific computing but do not scale well with dimension. In support of this prospect\, here I will review what is known about the trainability and accuracy of shallow neural networks\, which offer the simplest instance of nonlinear learning in functional spaces that are fundamentally different from classic approximation spaces. The dynamics of training in these spaces can be analyzed using tools from optimal transport and statistical mechanics\, which reveal when and how shallow neural networks can overcome the curse of dimensionality. I will also discuss how scientific computing problem in high-dimension once thought intractable can be revisited through the lens of these results\, focusing on applications related to (i) solving Fokker-Planck equations associated with high-dimensional systems displaying metastability and (ii) sampling Boltzmann-Gibbs distributions using generative models to assist MCMC methods.
URL:https://www.math.ens.psl.eu/evenement/machine-learning-and-applied-mathematics/
LOCATION:Amphi Jaurès (29 Rue d’Ulm)
CATEGORIES:Séminaire Data de l’ENS
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