Dropout Drops Double Descent

In this paper, we find and analyze that we can easily drop the double descent by only adding one dropout layer before the fully-connected linear layer. The surprising double-descent phenomenon has drawn public attention in recent years, making the prediction error rise and drop as we increase either sample or model size. The current paper shows that it is possible to alleviate these phenomena by using optimal dropout in the linear regression model and the nonlinear random feature regression, both theoretically and empirically. % ${y}=X{\beta}^0+{\epsilon}$ with $X\in\mathbb{R}^{n\times p}$. We obtain the optimal dropout hyperparameter by estimating the ground truth ${\beta}^0$ with generalized ridge typed estimator $\hat{{\beta}}=(X^TX+\alpha\cdot\mathrm{diag}(X^TX))^{-1}X^T{y}$. Moreover, we empirically show that optimal dropout can achieve a monotonic test error curve in nonlinear neural networks using Fashion-MNIST and CIFAR-10. Our results suggest considering dropout for risk curve scaling when meeting the peak phenomenon. In addition, we figure out why previous deep learning models do not encounter double-descent scenarios -- because we already apply a usual regularization approach like the dropout in our models. To our best knowledge, this paper is the first to analyze the relationship between dropout and double descent.