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Benign overfitting, the phenomenon where interpolating models generalize wellin the presence of noisy data, was first observed in neural network modelstrained with gradient descent. To better understand this empirical observation,we consider the generalization error of two-layer neural networks trained tointerpolation by gradient descent on the logistic loss following randominitialization. We assume the data comes from well-separated class-conditionallog-concave distributions and allow for a constant fraction of the traininglabels to be corrupted by an adversary. We show that in this setting, neuralnetworks exhibit benign overfitting: they can be driven to zero training error,perfectly fitting any noisy training labels, and simultaneously achieve minimaxoptimal test error. In contrast to previous work on benign overfitting thatrequire linear or kernel-based predictors, our analysis holds in a settingwhere both the model and learning dynamics are fundamentally nonlinear.

Benign Overfitting without Linearity: Neural Network Classifiers Trained by Gradient Descent for Noisy Linear Data