Title: Acutum: When Generalization Meets Adaptability. Abstract: In spite of the slow convergence, stochastic gradient descent (SGD) is still the most practical optimization method due to its outstanding generalization ability and simplicity. On the other hand, adaptive methods have attracted much more attention of optimization and machine learning communities, both for the leverage of life-long information and for the deep and fundamental mathematical theory. Taking the best of both worlds is the most exciting and challenging question in the field of optimization for machine learning. 

In this paper, we take a small step towards such ultimate goal. We revisit existing adaptive methods from a novel point of view, which reveals a fresh understanding of momentum. Our new intuition empowers us to remove the second moments in Adam without the loss of performance. Based on our view, we propose a new method, named acute adaptive momentum (Acutum). To the best of our knowledge, Acutum is the first adaptive gradient method without second moments. Experimentally, we demonstrate that our method has a faster convergence rate than Adam/Amsgrad, and generalizes as well as SGD with momentum. We also provide a convergence analysis of our proposed method to complement our intuition. 