Mathematical Foundations of Artificial Intelligence

We particularly focus on two interrelated research topics that fall into this broad template. The first one concerns how to accommodate symmetries explicitly in machine learning models. The second one concentrates on high-dimensional and large-scale optimization problems and the deployment of algorithms in modern computing systems. Our research topics include:

• Equivariance of neural networks
• Neural differential equations
• Learning on manifolds
• Compressive sensing
• Implicit regularization and theory of deep learning
• Distributed and federated optimization
• Non-convex and non-smooth optimization
• Operator splitting and variational inference
• Optimization with quantum computers