Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of non-equilibrium statistical physics. We show that, for large network width $m$, and large number of samples per input dimension $n/d$, the training dynamics exhibits a separation of timescales which implies: $(i)$~The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; $(ii)$~Inductive bias towards small complexity if the initialization has small enough complexity; $(iii)$~A dynamical decoupling between feature learning and overfitting regimes; $(iv)$~A non-monotone behavior of the test error, associated `feature unlearning' regime at large times.

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