Over-parameterized models, in particular deep networks, often exhibit a double descent phenomenon, where as a function of model size, error first decreases, increases, and decreases at last. This intriguing double descent behavior also occurs as a function of training epochs, and has been conjectured to arise because training epochs control the model complexity. In this paper, we show that such epoch-wise double descent arises for a different reason: It is caused by a superposition of two or more bias-variance tradeoffs that arise because different parts of the network are learned at different times, and eliminating this by proper scaling of stepsizes can significantly improve the early stopping performance. We show this analytically for i) linear regression, where differently scaled features give rise to a superposition of bias-variance tradeoffs, and for ii) a two-layer neural network, where the first and second layers each govern a bias-variance tradeoff. Inspired by this theory, we study a five-layer convolutional network empirically and show that eliminating epoch-wise double descent through adjusting stepsizes of different layers improves the early stopping performance significantly.

本文探讨了过度参数化模型，特别是深度神经网络，在训练期间错误率的演化现象，其原因是来自于不同部分在不同时期学习带来的偏差-方差权衡嵌套问题。通过合理调整步长，可以显著提高早停指标。

深度网络中的早停法：双重下降及其消除方法