## 3 événements

• Rough paths

### Jeudi 27 avril 10:30-11:30 - Gaultier Lambert - KTH Stockholm

CLT for Beta ensembles with a rate of convergence in Wasserstein 1 distance

Notes de dernières minutes : Work in collaboration with Christian Webb, Aalto University

• Séminaire exceptionnel

### Jeudi 27 avril 11:00-12:00 - Thirupathi GUDI (invité UMI IFCAM) - Indian Institute of Science, Bangalore

An energy space based approach for the finite element approximation of the Dirichlet boundary control problem

Lieu : Salle de Conférence (Bâtiment 1R3, 1er étage)

• Mathématiques de l’apprentissage

### Jeudi 27 avril 12:30-13:30 - François Malgouyres - Institut de Mathématiques de Toulouse

Stable recovery of the factors from a deep matrix product and application to convolutional network

Résumé : We study a deep matrix factorization problem. It takes as input a matrix $X$ obtained by multiplying $K$ matrices (called factors). Each factor is obtained by applying a fixed linear operator to a short vector of parameters satisfying a model (for instance sparsity, grouped sparsity, non-negativity, constraints defining a convolution network\ldots). We call the problem deep or multi-layer because the number of factors is not limited. In the practical situations we have in mind, we can typically have $K=10$ or $100$. This work aims at identifying conditions on the structure of the model that guarantees the stable recovery of the factors from the knowledge of $X$ and the model for the factors.
We provide necessary and sufficient conditions for the identifiability of the factors (up to a scale rearrangement). We also provide a necessary and sufficient condition called Deep Null Space Property (because of the analogy with the usual Null Space Property in the compressed sensing framework) which guarantees that even an inaccurate optimization algorithm for the factorization stably recovers the factors.
We illustrate the theory with a practical example where the deep factorization is a convolutional network.

Lieu : building 1R3, MIP conference room