Recent works have demonstrated that global covariance pooling (GCP) has the ability to improve performance of deep convolutional neural networks (CNNs) on visual classification task. Despite considerable advance, the reasons on effectiveness of GCP on deep CNNs have not been well studied. In this paper, we make an attempt to understand what deep CNNs benefit from GCP in a viewpoint of optimization. Specifically, we explore the effect of GCP on deep CNNs in terms of the Lipschitzness of optimization loss and the predictiveness of gradients, and show that GCP can make the optimization landscape more smooth and the gradients more predictive. Furthermore, we discuss the connection between GCP and second-order optimization for deep CNNs. More importantly, above findings can account for several merits of covariance pooling for training deep CNNs that have not been recognized previously or fully explored, including significant acceleration of network convergence (i.e., the networks trained with GCP can support rapid decay of learning rates, achieving favorable performance while significantly reducing number of training epochs), stronger robustness to distorted examples generated by image corruptions and perturbations, and good generalization ability to different vision tasks, e.g., object detection and instance segmentation. We conduct extensive experiments using various deep CNN models on diversified tasks, and the results provide strong support to our findings.
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