Global covariance pooling in convolutional neural networks has achieved impressive improvement over the classical first-order pooling. Recent works have shown matrix square root normalization plays a central role in achieving state-of-the-art performance. However, existing methods depend heavily on eigendecomposition (EIG) or singular value decomposition (SVD), suffering from inefficient training due to limited support of EIG and SVD on GPU. Towards addressing this problem, we propose an iterative matrix square root normalization method for fast end-to-end training of global covariance pooling networks. At the core of our method is a meta-layer designed with loop-embedded directed graph structure. The meta-layer consists of three consecutive nonlinear structured layers, which perform pre-normalization, coupled matrix iteration and post-compensation, respectively. Our method is much faster than EIG or SVD based ones, since it involves only matrix multiplications, suitable for parallel implementation on GPU. Moreover, the proposed network with ResNet architecture can converge in much less epochs, further accelerating network training. On large-scale ImageNet, we achieve competitive performance superior to existing counterparts. By finetuning our models pre-trained on ImageNet, we establish state-of-the-art results on three challenging fine-grained benchmarks. The source code and network models will be available at http://www.peihuali.org/iSQRT-COV
Classifying facial expressions into different categories requires capturing regional distortions of facial landmarks. We believe that second-order statistics such as covariance is better able to capture such distortions in regional facial fea- tures. In this work, we explore the benefits of using a man- ifold network structure for covariance pooling to improve facial expression recognition. In particular, we first employ such kind of manifold networks in conjunction with tradi- tional convolutional networks for spatial pooling within in- dividual image feature maps in an end-to-end deep learni…
Dalian University of Technology（大连理工大学）；Tianjin University（天津大学）
For video recognition task, a global representation summarizing the whole contents of the video snippets plays an important role for the final performance. However, existing video architectures usually generate it by using a simple, global average pooling (GAP) method, which has limited ability to capture complex dynamics of videos. For image recognition task, there exist evidences showing that covariance pooling has stronger representation ability than GAP. Unfortunately, such plain covariance pooling used in image recognition is an orderless representative, which cannot model spatio-temporal…
Tianjin University（天津大学）；Dalian University of Technology（大连理工大学）；Harbin Institute of Technology（哈尔滨工业大学）
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 …
The problem of multi-domain learning of deep networks is considered. An adaptive layer is induced per target domain and a novel procedure, denoted covariance normalization (CovNorm), proposed to reduce its parameters. CovNorm is a data driven method of fairly simple implementation, requiring two principal component analyzes (PCA) and fine-tuning of a mini-adaptation layer. Nevertheless, it is shown, both theoretically and experimentally, to have several advantages over previous approaches, such as batch normalization or geometric matrix approximations. Furthermore, CovNorm can be deployed both…
Tianjin University（天津大学）；Dalian University of Technology（大连理工大学）；Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong Polytechnic University（香港理工大学）
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-CO…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所人工智能研究中心）
Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods are applied to local features extracted from CNN models, the accuracy increases when the pooling function is back-propagatable and the feature-extraction model is learned in an end-to-end manner. Recently, the iterative polynomial approximation method for the matrix square root o…
Northeastern University（东北大学）；Information Sciences Institute, USC（南加州大学信息科学研究所）
Bilinear pooling has been recently proposed as a feature encoding layer, which can be used after the convolutional layers of a deep network, to improve performance in multiple vision tasks. Different from conventional global average pooling or fully connected layer, bilinear pooling gathers 2nd order information in a translation invariant fashion. However, a serious drawback of this family of pooling layers is their dimensionality explosion. Approximate pooling methods with compact properties have been explored towards resolving this weakness. Additionally, recent results have shown that signi…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering tasks among others. The resulting representation captures second-order statistics of convolutional features in a translationally invariant manner. In this paper we investigate various ways of normalizing these statistics to improve their representation power. In particular we find that the matrix square-root normalization offers significant improvements and…
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 grad…
The Fine-Grained Visual Categorization (FGVC) is challenging because the subtle inter-class variations are difficult to be captured. One notable research line uses the Global Covariance Pooling (GCP) layer to learn powerful representations with second-order statistics, which can effectively model inter-class differences. In our previous conference paper, we show that truncating small eigenvalues of the GCP covariance can attain smoother gradient and improve the performance on large-scale benchmarks. However, on fine-grained datasets, truncating the small eigenvalues would make the model fail t…
Data61/CSIRO（Data61/澳大利亚联邦科学与工业研究组织）；Australian National University（澳大利亚国立大学）
Power Normalizations (PN) are useful non-linear operators which tackle feature imbalances in classification problems. We study PNs in the deep learning setup via a novel PN layer pooling feature maps. Our layer combines the feature vectors and their respective spatial locations in the feature maps produced by the last convolutional layer of CNN into a positive definite matrix with second-order statistics to which PN operators are applied, forming so-called Second-order Pooling (SOP). As the main goal of this paper is to study Power Normalizations, we investigate the role and meaning of MaxExp …
Newcastle University（纽卡斯尔大学）；University of East Anglia（东英吉利大学）；Inception Institute of Artificial Intelligence（起源人工智能研究院）
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 …
Data61/CSIRO（Data61/联邦科学与工业研究组织）；Australian National University（澳大利亚国立大学）
Power Normalizations (PN) are very useful non-linear operators in the context of Bag-of-Words data representations as they tackle problems such as feature imbalance. In this paper, we reconsider these operators in the deep learning setup by introducing a novel layer that implements PN for non-linear pooling of feature maps. Specifically, by using a kernel formulation, our layer combines the feature vectors and their respective spatial locations in the feature maps produced by the last convolutional layer of CNN. Linearization of such a kernel results in a positive definite matrix capturing the…
Pohang University of Science and Technology（浦项科技大学）
For the stable optimization of deep neural networks, regularization methods such as dropout and batch normalization have been used in various tasks. Nevertheless, the correct position to apply dropout has rarely been discussed, and different positions have been employed depending on the practitioners. In this study, we investigate the correct position to apply dropout. We demonstrate that for a residual network with batch normalization, applying dropout at certain positions increases the performance, whereas applying dropout at other positions decreases the performance. Based on theoretical an…
University of Victoria（维多利亚大学）；Google Research（谷歌研究院）
Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution-they operate on individual data points with simple perceptrons and extract contextual information with global pooling. This can be achieved with a simple normalization of the feature maps, a global operation that is unaffected by the order. In this paper, we propose Attentive Context Normalization (ACN), a simple yet effective technique to build permutation-equivariant networks robust to outliers. Specifically, we show how to …
Dalian University of Technology（大连理工大学）；Harbin Institute of Technology（哈尔滨工业大学）
By stacking layers of convolution and nonlinearity, convolutional networks (ConvNets) effectively learn from low-level to high-level features and discriminative representations. Since the end goal of large-scale recognition is to delineate complex boundaries of thousands of classes, adequate exploration of feature distributions is important for realizing full potentials of ConvNets. However, state-of-the-art works concentrate only on deeper or wider architecture design, while rarely exploring feature statistics higher than first-order. We take a step towards addressing this problem. Our method…
Bilinear pooling achieves great success in fine-grained visual recognition (FGVC). Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features, but some problems, e.g., redundant information and over-fitting, remain to be resolved. In this paper, we propose an efficient Multi-Objective Matrix Normalization (MOMN) method that can simultaneously normalize a bilinear representation in terms of square-root, low-rank, and sparsity. These three regularizers can not only stabilize the second-order information, but also compact the bili…
Dalian University of Technology（大连理工大学）；Tianjin University（天津大学）
Deep Convolutional Networks (ConvNets) are fundamental to, besides large-scale visual recognition, a lot of vision tasks. As the primary goal of the ConvNets is to characterize complex boundaries of thousands of classes in a high-dimensional space, it is critical to learn higher-order representations for enhancing non-linear modeling capability. Recently, Global Second-order Pooling (GSoP), plugged at the end of networks, has attracted increasing attentions, achieving much better performance than classical, first-order networks in a variety of vision tasks. However, how to effectively introduc…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Data61/CSIRO（Data61/联邦科学与工业研究组织）；Australian National University（澳大利亚国立大学）
Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization afte…
University of Saskatchewan（萨斯喀彻温大学）；University of Tulane（杜兰大学）
Breast cancer is one of the most common causes of cancer-related death in women worldwide. Early and accurate diagnosis of breast cancer may significantly increase the survival rate of patients. In this study, we aim to develop a fully automatic, deep learning-based, method using descriptor features extracted by Deep Convolutional Neural Network (DCNN) models and pooling operation for the classification of hematoxylin and eosin stain (H&E) histological breast cancer images provided as a part of the International Conference on Image Analysis and Recognition (ICIAR) 2018 Grand Challenge on BreAs…
Zhejiang University（浙江大学）；Ping An Technology（平安科技）；Chinese Academy of Sciences（中国科学院）；Xi’an Jiaotong University（西安交通大学）
This study explores a simple but strong baseline for person re-identification (ReID). Person ReID with deep neural networks has progressed and achieved high performance in recent years. However, many state-of-the-art methods design complex network structures and concatenate multi-branch features. In the literature, some effective training tricks briefly appear in several papers or source codes. The present study collects and evaluates these effective training tricks in person ReID. By combining these tricks, the model achieves 94.5% rank-1 and 85.9% mean average precision on Market1501 with on…
DPNet: Dynamic Pooling Network for Tiny Object Detection
School of Computer Science, Beijing University of Posts and Telecommunications（北京邮电大学计算机科学学院）；Research Center for Space Computing System, Zhejiang Lab（浙江实验室空间计算系统研究中心）；SWJTU-LEEDS Joint School, Southwest Jiaotong University（西南交通大学SWJTU-LEEDS联合学院）；Guangdong Zhiyun City construction Technology Co., LTD（广东智云城市建设技术有限公司）；Department of Control Science and Engineering, College of Electronic and Information Engineering, Tongji University（同济大学控制科学与工程系）；Key Laboratory of Maritime Intelligent Network Information Technology, Ministry of Education, Hohai University（河海大学航海智能网络信息科技重点实验室）
Inserting an SVD meta-layer into neural networks is prone to make the covariance ill-conditioned, which could harm the model in the training stability and generalization abilities. In this paper, we systematically study how to improve the covariance conditioning by enforcing orthogonality to the Pre-SVD layer. Existing orthogonal treatments on the weights are first investigated. However, these techniques can improve the conditioning but would hurt the performance. To avoid such a side effect, we propose the Nearest Orthogonal Gradient (NOG) and Optimal Learning Rate (OLR). The effectiveness of…
University of Trento（特伦托大学）；Beijing Jiaotong University（北京交通大学）
Inserting an SVD meta-layer into neural networks is prone to make the covariance ill-conditioned, which could harm the model in the training stability and generalization abilities. In this paper, we systematically study how to improve the covariance conditioning by enforcing orthogonality to the Pre-SVD layer. Existing orthogonal treatments on the weights are first investigated. However, these techniques can improve the conditioning but would hurt the performance. To avoid such a side effect, we propose the Nearest Orthogonal Gradient (NOG) and Optimal Learning Rate (OLR). The effectiveness of…
Vehicle re-identification is an important computer vision task where the objective is to identify a specific vehicle among a set of vehicles seen at various viewpoints. Recent methods based on deep learning utilize a global average pooling layer after the backbone feature extractor, however, this ignores any spatial reasoning on the feature map. In this paper, we propose local graph aggregation on the backbone feature map, to learn associations of local information and hence improve feature learning as well as reduce the effects of partial occlusion and background clutter. Our local graph aggr…
Voronoi-based Second-order Descriptor with Whitened Metric in LiDAR Place Recognition
Interdisciplinary Program in Neuroscience（神经科学跨学科项目）；Département d’Informatique, École Normale Supérieure (ENS)（高等师范学院计算机系）；Department of Computing, Imperial College London（伦敦帝国理工学院计算系）；Dept. of Computer Science and Engineering, Seoul National University（首尔国立大学计算机科学与工程系）
This paper reports a novel deep architecture referred to as Maxout network In Network (MIN), which can enhance model discriminability and facilitate the process of information abstraction within the receptive field. The proposed network adopts the framework of the recently developed Network In Network structure, which slides a universal approximator, multilayer perceptron (MLP) with rectifier units, to exact features. Instead of MLP, we employ maxout MLP to learn a variety of piecewise linear activation functions and to mediate the problem of vanishing gradients that can occur when using recti…
Computing the matrix square root and its inverse in a differentiable manner is important in a variety of computer vision tasks. Previous methods either adopt the Singular Value Decomposition (SVD) to explicitly factorize the matrix or use the Newton-Schulz iteration (NS iteration) to derive the approximate solution. However, both methods are not computationally efficient enough in either the forward pass or the backward pass. In this paper, we propose two more efficient variants to compute the differentiable matrix square root and the inverse square root. For the forward propagation, one metho…
University of Chinese Academy of Sciences（中国科学院大学）；School of Technology, Nanjing Audit University（南京审计大学技术学院）；Department of Medicine, Indiana University（印第安纳大学医学系）
The region-based Convolutional Neural Network (CNN) detectors such as Faster R-CNN or R-FCN have already shown promising results for object detection by combining the region proposal subnetwork and the classification subnetwork together. Although R-FCN has achieved higher detection speed while keeping the detection performance, the global structure information is ignored by the position-sensitive score maps. To fully explore the local and global properties, in this paper, we propose a novel fully convolutional network, named as CoupleNet, to couple the global structure with local parts for obj…
Baze University（巴泽大学）；The University of the West of England（西英格兰大学）
Deep networks have achieved huge successes in application domains like object and face recognition. The performance gain is attributed to different facets of the network architecture such as: depth of the convolutional layers, activation function, pooling, batch normalization, forward and back propagation and many more. However, very little emphasis is made on the preprocessors. Therefore, in this paper, the network's preprocessing module is varied across different preprocessing approaches while keeping constant other facets of the network architecture, to investigate the contribution preproce…
In this paper, we propose a novel Discrete Cosine Transform (DCT)-based neural network layer which we call DCT-perceptron to replace the $3\times3$ Conv2D layers in the Residual neural Network (ResNet). Convolutional filtering operations are performed in the DCT domain using element-wise multiplications by taking advantage of the Fourier and DCT Convolution theorems. A trainable soft-thresholding layer is used as the nonlinearity in the DCT perceptron. Compared to ResNet's Conv2D layer which is spatial-agnostic and channel-specific, the proposed layer is location-specific and channel-specific.…
We report that a very high accuracy on the MNIST test set can be achieved by using simple convolutional neural network (CNN) models. We use three different models with 3x3, 5x5, and 7x7 kernel size in the convolution layers. Each model consists of a set of convolution layers followed by a single fully connected layer. Every convolution layer uses batch normalization and ReLU activation, and pooling is not used. Rotation and translation is used to augment training data, which is frequently used in most image classification tasks. A majority voting using the three models independently trained on…
