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In this work, we provide a characterization of the feature-learning processin two-layer ReLU networks trained by gradient descent on the logistic lossfollowing random initialization. We consider data with binary labels that aregenerated by an XOR-like function of the input features. We permit a constantfraction of the training labels to be corrupted by an adversary. We show that,although linear classifiers are no better than random guessing for thedistribution we consider, two-layer ReLU networks trained by gradient descentachieve generalization error close to the label noise rate. We develop a novelproof technique that shows that at initialization, the vast majority of neuronsfunction as random features that are only weakly correlated with usefulfeatures, and the gradient descent dynamics 'amplify' these weak, randomfeatures to strong, useful features.

Random Feature Amplification: Feature Learning and Generalization in Neural Networks