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Register a new userWhat Deep CNNs Benefit from Global Covariance Pooling: An Optimization Perspective
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Qilong Wang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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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Compared with global average pooling in existing deep convolutional neural networks (CNNs), global covariance pooling can capture richer statistics of deep features, having potential for improving representation and generalization abilities of deep CNNs. However, integration of global covariance pooling into deep CNNs brings two challenges: (1) robust covariance estimation given deep features of high dimension and small sample size; (2) appropriate usage of geometry of covariances. To address these challenges, we propose a global Matrix Power Normalized COVariance (MPN-COV) Pooling. Our MPN-COV conforms to a robust covariance estimator, very suitable for scenario of high dimension and small sample size. It can also be regarded as Power-Euclidean metric between covariances, effectively exploiting their geometry. Furthermore, a global Gaussian embedding network is proposed to incorporate first-order statistics into MPN-COV. For fast training of MPN-COV networks, we implement an iterative matrix square root normalization, avoiding GPU unfriendly eigen-decomposition inherent in MPN-COV. Additionally, progressive 1x1 convolutions and group convolution are introduced to compress covariance representations. The proposed methods are highly modular, readily plugged into existing deep CNNs. Extensive experiments are conducted on large-scale object classification, scene categorization, fine-grained visual recognition and texture classification, showing our methods outperform the counterparts and obtain state-of-the-art performance.
Deep convolutional neural networks learn extremely powerful image representations, yet most of that power is hidden in the millions of deep-layer parameters. What exactly do these parameters represent? Recent work has started to analyse CNN representations, finding that, e.g., they are invariant to some 2D transformations Fischer et al. (2014), but are confused by particular types of image noise Nguyen et al. (2014). In this work, we delve deeper and ask: how invariant are CNNs to object-class variations caused by 3D shape, pose, and photorealism?
Learning discriminative and invariant feature representation is the key to visual image categorization. In this article, we propose a novel invariant deep compressible covariance pooling (IDCCP) to solve nuisance variations in aerial scene categorization. We consider transforming the input image according to a finite transformation group that consists of multiple confounding orthogonal matrices, such as the D4 group. Then, we adopt a Siamese-style network to transfer the group structure to the representation space, where we can derive a trivial representation that is invariant under the group action. The linear classifier trained with trivial representation will also be possessed with invariance. To further improve the discriminative power of representation, we extend the representation to the tensor space while imposing orthogonal constraints on the transformation matrix to effectively reduce feature dimensions. We conduct extensive experiments on the publicly released aerial scene image data sets and demonstrate the superiority of this method compared with state-of-the-art methods. In particular, with using ResNet architecture, our IDCCP model can reduce the dimension of the tensor representation by about 98% without sacrificing accuracy (i.e., <0.5%).
Global covariance pooling (GCP) aims at exploiting the second-order statistics of the convolutional feature. Its effectiveness has been demonstrated in boosting the classification performance of Convolutional Neural Networks (CNNs). Singular Value Decomposition (SVD) is used in GCP to compute the matrix square root. However, the approximate matrix square root calculated using Newton-Schulz iteration cite{li2018towards} outperforms the accurate one computed via SVD cite{li2017second}. We empirically analyze the reason behind the performance gap from the perspectives of data precision and gradient smoothness. Various remedies for computing smooth SVD gradients are investigated. Based on our observation and analyses, a hybrid training protocol is proposed for SVD-based GCP meta-layers such that competitive performances can be achieved against Newton-Schulz iteration. Moreover, we propose a new GCP meta-layer that uses SVD in the forward pass, and Pade Approximants in the backward propagation to compute the gradients. The proposed meta-layer has been integrated into different CNN models and achieves state-of-the-art performances on both large-scale and fine-grained datasets.
In this paper, we challenge the common assumption that collapsing the spatial dimensions of a 3D (spatial-channel) tensor in a convolutional neural network (CNN) into a vector via global pooling removes all spatial information. Specifically, we demonstrate that positional information is encoded based on the ordering of the channel dimensions, while semantic information is largely not. Following this demonstration, we show the real world impact of these findings by applying them to two applications. First, we propose a simple yet effective data augmentation strategy and loss function which improves the translation invariance of a CNNs output. Second, we propose a method to efficiently determine which channels in the latent representation are responsible for (i) encoding overall position information or (ii) region-specific positions. We first show that semantic segmentation has a significant reliance on the overall position channels to make predictions. We then show for the first time that it is possible to perform a `region-specific attack, and degrade a networks performance in a particular part of the input. We believe our findings and demonstrated applications will benefit research areas concerned with understanding the characteristics of CNNs.
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