Title: Deep Active Learning by Leveraging Training Dynamics. Abstract: Active learning theories and methods have been extensively studied in classical statistical learning settings. However, deep active learning, i.e., active learning with deep learning models, is usually based on empirical criteria without solid theoretical justiﬁcation, thus suffering from heavy doubts when some of those fail to provide beneﬁts in applications. In this paper, by exploring the connection between the generalization performance and the training dynamics, we propose a theory-driven deep active learning method (dynamicAL) which selects samples to maximize training dynamics. In particular, we prove that convergence speed of training and the generalization performance is positively correlated under the ultra-wide condition and show that maximizing the training dynamics leads to a better generalization performance. Further on, to scale up to large deep neural networks and data sets, we introduce two relaxations for the subset selection problem and reduce the time complexity from polynomial to constant. Empirical results show that dynamicAL not only outperforms the other baselines consistently but also scales well on large deep learning models. We hope our work inspires more attempts in bridging the theoretical ﬁndings of deep networks and practical impacts in deep active learning applications.