Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss; yet surprisingly, they possess near-optimal prediction performance, contradicting classical learning theory. We examine how these benign overfitting phenomena occur in a two-layer neural network setting where sample covariates are corrupted with noise. We address the high dimensional regime, where the data dimension $d$ grows with the number $n$ of data points. Our analysis combines an upper bound on the bias with matching upper and lower bounds on the variance of the interpolator (an estimator that interpolates the data). These results indicate that the excess learning risk of the interpolator decays under mild conditions. We further show that it is possible for the two-layer ReLU network interpolator to achieve a near minimax-optimal learning rate, which to our knowledge is the first generalization result for such networks. Finally, our theory predicts that the excess learning risk starts to increase once the number of parameters $s$ grows beyond $O(n^2)$, matching recent empirical findings.

本研究探讨了现代机器学习模型中广泛存在的过度拟合现象及理论预测，表明超学习风险会在满足一定条件的情况下逐渐减小，并且在两层神经网络中使用ReLU激活函数的情况下具有近最小化学习率的能力。同时，还发现当网络参数数量超过O(n^2)时，超学习风险开始增加，这与最近的实证结果相符。

神经网络中良性过拟合现象的理解探讨