Andrea Montanari: The Phase Diagram of 2-Layer Neural Networks (September 24, 2026)

Classical statistical models are constructed so that either the number of parameters is small with respect to the sample size, or the regularization is strong enough so that their “effective dimension” is small. In contrast, modern machine learning models are vastly miss-specified and overparametrized, and only very loosely regularized. These models are learnt using empirical risk minimization, but the empirical risk function has many near-global optima which are very far from each other in parameter space. How can we make sense of the good statistical properties of these models? Andrea Montanari will summarize what we learned over the years by studying a simple and yet extremely rich setting: learning in two-layer networks. For more information please visit: https://www.simonsfoundation.org/even...