Adaptive optimization methods have been widely used in deep learning. They scale the learning rates adaptively according to the past gradient, which has been shown to be effective to accelerate the convergence. However, they suffer from poor generalization performance compared with SGD. Recent studies point that smoothing exponential gradient noise leads to generalization degeneration phenomenon. Inspired by this, we propose AdaL, with a transformation on the original gradient. AdaL accelerates the convergence by amplifying the gradient in the early stage, as well as dampens the oscillation and stabilizes the optimization by shrinking the gradient later. Such modification alleviates the smoothness of gradient noise, which produces better generalization performance. We have theoretically proved the convergence of AdaL and demonstrated its effectiveness on several benchmarks.

Existing rotated object detectors are mostly inherited from the horizontal detection paradigm, as the latter has evolved into a well-developed area. However, these detectors are difficult to perform prominently in high-precision detection due to the limitation of current regression loss design, especially for objects with large aspect ratios. Taking the perspective that horizontal detection is a special case for rotated object detection, in this paper, we are motivated to change the design of rotation regression loss from induction paradigm to deduction methodology, in terms of the relation between rotation and horizontal detection. We show that one essential challenge is how to modulate the coupled parameters in the rotation regression loss, as such the estimated parameters can influence to each other during the dynamic joint optimization, in an adaptive and synergetic way. Specifically, we first convert the rotated bounding box into a 2-D Gaussian distribution, and then calculate the Kullback-Leibler Divergence (KLD) between the Gaussian distributions as the regression loss. By analyzing the gradient of each parameter, we show that KLD (and its derivatives) can dynamically adjust the parameter gradients according to the characteristics of the object. It will adjust the importance (gradient weight) of the angle parameter according to the aspect ratio. This mechanism can be vital for high-precision detection as a slight angle error would cause a serious accuracy drop for large aspect ratios objects. More importantly, we have proved that KLD is scale invariant.

Boundary discontinuity and its inconsistency to the final detection metric have been the bottleneck for rotating detection regression loss design. In this paper, we propose a novel regression loss based on Gaussian Wasserstein distance as a fundamental approach to solve the problem. Specifically, the rotated bounding box is converted to a 2-D Gaussian distribution, which enables to approximate the indifferentiable rotational IoU induced loss by the Gaussian Wasserstein distance (GWD) which can be learned efficiently by gradient back-propagation. GWD can still be informative for learning even there is no overlapping between two rotating bounding boxes which is often the case for small object detection. Thanks to its three unique properties, GWD can also elegantly solve the boundary discontinuity and square-like problem regardless how the bounding box is defined. Experiments on five datasets using different detectors show the effectiveness of our approach. Codes are available at https://github.com/yangxue0827/RotationDetection.