Understanding machine learning via exactly solvable statistical physics models

The affinity between statistical physics and machine learning has long history, this is reflected even in the machine learning terminology that is in part adopted from physics. 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 learning algorithm.