Towards demystifying over-parameterization and early stopping in deep learning
Many modern neural networks are trained in an over-parameterized regime where the parameters of the model exceed the size of the training dataset. Due to their over-parameterized nature these models in principle have the capacity to (over)fit any set of labels including pure noise. Despite this high fitting capacity, somewhat paradoxically, models trained via first-order methods (often with early stopping) continue to predict well on yet unseen test data. In this talk I will discuss some results aimed at demystifying such phenomena by demonstrating that gradient methods enjoy a few intriguing properties: (1) when initialized at random the iterates converge at a geometric rate to a global optima, (2) among all global optima of the loss the iterates converge to one with good generalization capability, (3) with early-stopping are provably robust to noise/corruption/shuffling on a fraction of the labels with these algorithms only fitting to the correct labels and ignoring the corrupted labels.