The research school "High Dimensional Approximation and Deep Learning" will be held in Nantes from May 16 to 20, 2022.

This school addresses the mathematical foundations of high-dimensional approximation and statistical learning, with particular attention to nonlinear approximation, model reduction, tensors and neural networks.

The research school is intended for PhD students, young researchers and confirmed researchers interested in these themes.

The school will feature four courses given by experts in the mathematics of approximation and learning:

• Course 1: Albert Cohen, Approximation of multivariate functions: reduced modeling and recovery from uncomplete measurements
• Course 2: Lars Grasedyck, Approximation with Hierarchical Low Rank Tensors
• Course 3: Sophie Langer, On the statistical theory of deep learning
• Course 4: Philipp Petersen, Approximation theory of deep neural networks,

Course 2 will be complemented by practical sessions handled by Sebastian Krämer.

Invited talks will complement courses on recent advances in learning algorithms and approximation theory of neural networks.

•  Sébastien Gerchinovitz, Approximation lower bounds in L^p norm, with applications to feedforward neural networks
•  Stéphane Chrétien, Benign overfitting : analysis of the generalisation paradox

Keywords: approximation and learning in high dimension, tensors, neural networks, deep learning, model reduction, inverse problems