Modern neural networks are typically trained in an over-parameterized regime where the parameters of the model far exceed the size of the training data. Due to over-parameterization these neural networks in principle have the capacity to (over)fit any set of labels including pure noise. Despite this high fitting capacity, somewhat paradoxically, neural network models trained via first-order methods continue to predict well on yet unseen test data. In this paper we take a step towards demystifying this phenomena. In particular we show that first order methods such as gradient descent are provably robust to noise/corruption on a constant fraction of the labels despite over-parametrization under a rich dataset model. In particular: i) First, we show that in the first few iterations where the updates are still in the vicinity of the initialization these algorithms only fit to the correct labels essentially ignoring the noisy labels. ii) Secondly, we prove that to start to overfit to the noisy labels these algorithms must stray rather far from from the initial model which can only occur after many more iterations. Together, these show that gradient descent with early stopping is provably robust to label noise and shed light on empirical robustness of deep networks as well as commonly adopted heuristics to prevent overfitting.

本文研究神经网络的训练，证明使用梯度下降法可以在一定的噪声或污染下保证稳健性，避免过拟合。

早停梯度下降在过度参数化的神经网络上被证明对标签噪声具有鲁棒性