We are looking for PhD students at the University of Edinburgh for research focused on: Machine learning and optimization algorithms, Generative AI and artificial data, Privacy, fairness and explainability, Topological and Geometric data analysis and other similar areas.

The affinity between statistical physics and machine learning has a long history. I will describe the main lines of this long-lasting friendship in the context of current theoretical challenges and open questions about deep learning. Theoretical physics often proceeds in terms of solvable synthetic models, I will describe the related line of work on solvable models of simple feed-forward neural networks. I will highlight a path forward to capture the subtle interplay between the structure of the data, the architecture of the network, and the optimization algorithms commonly used for learning.