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We consider a one-hidden-layer leaky ReLU network of arbitrary width trainedby stochastic gradient descent (SGD) following an arbitrary initialization. Weprove that SGD produces neural networks that have classification accuracycompetitive with that of the best halfspace over the distribution for a broadclass of distributions that includes log-concave isotropic and hard margindistributions. Equivalently, such networks can generalize when the datadistribution is linearly separable but corrupted with adversarial label noise,despite the capacity to overfit. To the best of our knowledge, this is thefirst work to show that overparameterized neural networks trained by SGD cangeneralize when the data is corrupted with adversarial label noise.

Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise