  Due to its simplicity and outstanding ability to generalize, stochastic
gradient descent (SGD) is still the most widely used optimization method
despite its slow convergence. Meanwhile, adaptive methods have attracted rising
attention of optimization and machine learning communities, both for the
leverage of life-long information and for the profound 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. Along
this line, we revisited existing adaptive gradient methods from a novel
perspective, refreshing understanding of second moments. Our new perspective
empowers us to attach the properties of second moments to the first moment
iteration, and to propose a novel first moment optimizer,
\emph{Angle-Calibrated Moment method} (\method). Our theoretical results show
that \method is able to achieve the same convergence rate as mainstream
adaptive methods. Furthermore, extensive experiments on CV and NLP tasks
demonstrate that \method has a comparable convergence to SOTA Adam-type
optimizers, and gains a better generalization performance in most cases.
