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Progress and hurdles in the statistical mechanics of deep learning
Since the 80s, the statistical mechanics of learning studies simple solvable models of learning with tools from the physics of disordered systems. An original feature of the approach is to focus on typical performances rather than strict "worst-case" bounds. As such, it carries promises for understanding the generalization ability of deep neural networks with their enormous number of parameters relative to training data. I will present recent progress in two primary directions: taking into account the structure of data in generalization analyses and tackling deeper architectures.