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 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) 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.
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