Easy, Hard, Impossible: Phase Transitions in Learning

When your model fails, are you short of data or short of computation? Those look identical from the outside and have completely different fixes. This path builds the statistical physics of computation, the field that made the distinction precise: planted models and the high-dimensional limit, the three-phase structure where information can be present while every efficient algorithm fails, the message-passing algorithms that reach the computational limit and predict their own error exactly, and what genuinely transfers to deep learning.