Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks

TL;DR

This paper proves that early stopping in gradient descent training makes overparameterized neural networks robust to label noise, explaining why they generalize well despite their capacity to fit noisy data.

Contribution

It provides the first theoretical proof that early stopping in gradient descent ensures robustness to label noise in overparameterized neural networks.

Findings

Gradient descent initially fits only correct labels near initialization.

Overfitting noisy labels requires significant deviation from initialization.

Early stopping prevents overfitting to noisy labels, ensuring robustness.

Abstract

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