Title: On Optimal Early Stopping: Overparametrization versus Underparametrization. Abstract: Early stopping is a simple and widely used method to prevent over-training neural networks. We develop theoretical results to reveal the relationship between optimal early stopping time and model dimension as well as sample size of the dataset for certain linear regression models. Our results demonstrate two very different behaviors when the model dimension exceeds the number of features versus the opposite scenario. While most previous works on linear models focus on the latter setting, we observe that in common deep learning tasks, the dimension of the model often exceeds the number of features arising from data. We demonstrate experimentally that our theoretical results on optimal early stopping time corresponds to the training process of deep neural network. Moreover, we study the effect of early stopping on generalization and demonstrate that optimal early stopping can help mitigate ''descent'' in various settings.