- Date de réalisation : 3 Juillet 2019
- Lieu de réalisation : École Normale Supérieure, Paris.
- Durée du programme : 0 min
- Classification Dewey : Probabilités, Statistiques mathématiques, Mathématiques appliquées
- Auteur(s) : Zdeborová Lenka
- producteur : Boyer Claire, Chafaï Djalil, Lehec Joseph
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Zdeborová - Loss landscape and behaviour of algorithms in the spiked matrix-tensor model
A key question of current interest is: How are properties of optimization and sampling algorithms influenced by the properties of the loss function in noisy high-dimensional non-convex settings? Answering this question for deep neural networks is a landmark goal of many ongoing works. In this talk I will answer this question in unprecedented detail for the spiked matrix-tensor model. Information theoretic limits, and Kac-Rice analysis of the loss landscapes, will be compared to the analytically studied performance of message passing algorithms, of the Langevin dynamics and of the gradient flow. Several rather non-intuitive results will be unveiled and explained.