We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification. In particular, we consider linearly separable data for which a relatively small proportion of labels are corrupted or flipped. We identify conditions on the margin of the clean data that give rise to three distinct training outcomes: benign overfitting, in which zero loss is achieved and with high probability test data is classified correctly; overfitting, in which zero loss is achieved but test data is misclassified with probability lower bounded by a constant; and non-overfitting, in which clean points, but not corrupt points, achieve zero loss and again with high probability test data is classified correctly. Our analysis provides a fine-grained description of the dynamics of neurons throughout training and reveals two distinct phases: in the first phase clean points achieve close to zero loss, in the second phase clean points oscillate on the boundary of zero loss while corrupt points either converge towards zero loss or are eventually zeroed by the network. We prove these results using a combinatorial approach that involves bounding the number of clean versus corrupt updates across these phases of training.

本文探讨了使用梯度下降和hinge loss在嘈杂数据上训练的两层ReLU网络的良性过拟合问题，研究了线性可分数据，给出了干净数据边距的条件，得到了良性过拟合，过拟合和非过拟合三种不同的情况，并揭示了神经元训练过程中的两个不同阶段。

使用铰链损失函数训练浅层ReLU网络的噪声数据：过拟合何时发生且是否良性？