In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed independently for each kernel. However, the deformation may be spatially smooth over the neighboring kernels. This means that max pooling is too flexible to compensate for actual deformations. In other words, its excessive flexibility risks canceling the essential spatial differences between classes. In this paper, we propose regularized pooling, which enables the value selection direction in the pooling operation to be spatially smooth across adjacent kernels so as to compensate only for actual deformations. The results of experiments on handwritten character images and texture images showed that regularized pooling not only improves recognition accuracy but also accelerates the convergence of learning compared with conventional pooling operations.
Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical fundamentals, its practical implementations often depend on empirical mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In this work, we develop a novel and generalized global pooling framework through the lens of optimal transport. The proposed framework is interpretable from the perspective of expectation-maximization. Essentially, it aims at…
Yale University（耶鲁大学）；Yale School of Medicine（耶鲁大学医学院）；Facebook AI Research（Facebook人工智能研究院）
Understanding how certain brain regions relate to a specific neurological disorder has been an important area of neuroimaging research. A promising approach to identify the salient regions is using Graph Neural Networks (GNNs), which can be used to analyze graph structured data, e.g. brain networks constructed by functional magnetic resonance imaging (fMRI). We propose an interpretable GNN framework with a novel salient region selection mechanism to determine neurological brain biomarkers associated with disorders. Specifically, we design novel regularized pooling layers that highlight salient…
Max- and average-pooling are the most popular pooling methods for downsampling in convolutional neural networks. In this paper, we compare different pooling methods that generalize both max- and average-pooling. Furthermore, we propose another method based on a smooth approximation of the maximum function and put it into context with related methods. For the comparison, we use a VGG16 image classification network and train it on a large dataset of natural high-resolution images (Google Open Images v5). The results show that none of the more sophisticated methods perform significantly better in…
Image classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable relative distance towards each other. Various convolutional neural network image classifiers are introduced and compared in view of their rate of convergence. The finite sample size performance of the estimates is analyzed by applying them to simulated and real data.
Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weig…
Many theories have emerged which investigate how in- variance is generated in hierarchical networks through sim- ple schemes such as max and mean pooling. The restriction to max/mean pooling in theoretical and empirical studies has diverted attention away from a more general way of generating invariance to nuisance transformations. We con- jecture that hierarchically building selective invariance (i.e. carefully choosing the range of the transformation to be in- variant to at each layer of a hierarchical network) is im- portant for pattern recognition. We utilize a novel pooling layer called a…
We present generalized versions of the commonly used maximum pooling operation: $k$th maximum and sorted pooling operations which selects the $k$th largest response in each pooling region, selecting locally consistent features of the input images. This method is able to increase the generalization power of a network and can be used to decrease training time and error rate of networks and it can significantly improve accuracy in case of training scenarios where the amount of available data is limited, like one-shot learning scenarios
Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor alpha. The amazing by-product of discarding 75% of your data is that you build into the network a degree of invariance with respect to translations and elastic distortions. However, if you simply alternate convolutional layers with max-pooling layers, performance is limited due to the rapid reduction in spatial size, and the disjoint nature of t…
From Correlation to Causation: Max-Pooling-Based Multi-Instance Learning Leads to More Robust Whole Slide Image Classification
UniSA STEM, University of South Australia（南澳大利亚大学STEM学院）；School of Computer Science and Engineering, Southeast University（东南大学计算机科学与工程学院）；Key Lab. of Computer Network and Information Integration (Southeast University), MoE, China（计算机网络与信息集成重点实验室（东南大学），教育部，中国）；School of Information and Physical Sciences, The University of Newcastle（新castle大学信息与物理科学学院）；Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（穆罕默德·本·扎耶德人工智能大学）
State-of-the-art patch-based image representations involve a pooling operation that aggregates statistics computed from local descriptors. Standard pooling operations include sum- and max-pooling. Sum-pooling lacks discriminability because the resulting representation is strongly influenced by frequent yet often uninformative descriptors, but only weakly influenced by rare yet potentially highly-informative ones. Max-pooling equalizes the influence of frequent and rare descriptors but is only applicable to representations that rely on count statistics, such as the bag-of-visual-words (BOV) and…
NIRMAL Pooling: An Adaptive Max Pooling Approach with Non-linear Activation for Enhanced Image Classification
ThinkAI - A Machine Learning Community（ThinkAI - 一个机器学习社区）；Guru Nanak Institute of Technology（古鲁纳克技术学院）；Department of Computer Science, Narayan Zantye College（计算机科学系，纳拉扬赞蒂学院）；NIIT Foundation（NIIT基金会）；Dayananda Sagar College of Engineering（Dayananda Sagar工程学院）；IILM；Sri Balaji University（Sri Balaji大学）；University of Calcutta（加尔各答大学）；Mardin Artuklu University（马林艺术鲁大学）；City University of Hong Kong（香港城市大学）；Yenepoya (Deemed to be University)（Yenepoya（认定大学））；Aston University（阿斯顿大学）；Delhi Technical Campus（德里技术校区）；Lovely Professional University（洛丽专业大学）
Xinjiang University（新疆大学）；Software College, Xinjiang University（新疆大学软件学院）；Network Center, Xinjiang University（新疆大学网络中心）
To better retain the deep features of an image and solve the sparsity problem of the end-to-end segmentation model, we propose a new deep convolutional network model for medical image pixel segmentation, called MC-Net. The core of this network model consists of four parts, namely, an encoder network, a multiple max-pooling integration module, a cross multiscale deconvolution decoder network and a pixel-level classification layer. In the network structure of the encoder, we use multiscale convolution instead of the traditional single-channel convolution. The multiple max-pooling integration mod…
Pooling is essentially an operation from the field of Mathematical Morphology, with max pooling as a limited special case. The more general setting of MorphPooling greatly extends the tool set for building neural networks. In addition to pooling operations, encoder-decoder networks used for pixel-level predictions also require unpooling. It is common to combine unpooling with convolution or deconvolution for up-sampling. However, using its morphological properties, unpooling can be generalised and improved. Extensive experimentation on two tasks and three large-scale datasets shows that morpho…
Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of …
Harbin Institute of Technology（哈尔滨工业大学）；Peking University（北京大学）
In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convolution are popular pooling methods. Since the pooling is a lossy procedure, a motivation of our work is to design a new pooling approach for less lossy in the dimensionality reduction. Inspired by the Fourier spectral pooling(FSP) proposed by Rippel et. al. [1], we present the Hartle…
University of Liège（列日大学）；University of Louvain（鲁汶大学）；University of Sheffield（谢菲尔德大学）
In the framework of convolutional neural networks, downsampling is often performed with an average-pooling, where all the activations are treated equally, or with a max-pooling operation that only retains an element with maximum activation while discarding the others. Both of these operations are restrictive and have previously been shown to be sub-optimal. To address this issue, a novel pooling scheme, named\emph{ ordinal pooling}, is introduced in this work. Ordinal pooling rearranges all the elements of a pooling region in a sequence and assigns a different weight to each element based upon…
Pooling is a ubiquitous operation in image processing algorithms that allows for higher-level processes to collect relevant low-level features from a region of interest. Currently, max-pooling is one of the most commonly used operators in the computational literature. However, it can lack robustness to outliers due to the fact that it relies merely on the peak of a function. Pooling mechanisms are also present in the primate visual cortex where neurons of higher cortical areas pool signals from lower ones. The receptive fields of these neurons have been shown to vary according to the contrast …
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the common maximum value selection and mean value operations, not to mention providing a function that allows different functions to be selected through changing parameters. Additional neural networks are used to estimate the parameters of these pooling functions.Consequently, pooling layers may require supplementary parameters to increase the complexity of the…
We present a fast algorithm for training MaxPooling Convolutional Networks to segment images. This type of network yields record-breaking performance in a variety of tasks, but is normally trained on a computationally expensive patch-by-patch basis. Our new method processes each training image in a single pass, which is vastly more efficient. We validate the approach in different scenarios and report a 1500-fold speed-up. In an application to automated steel defect detection and segmentation, we obtain excellent performance with short training times.
In the framework of convolutional neural networks that lie at the heart of deep learning, downsampling is often performed with a max-pooling operation that only retains the element with maximum activation, while completely discarding the information contained in other elements in a pooling region. To address this issue, a novel pooling scheme, Ordinal Pooling Network (OPN), is introduced in this work. OPN rearranges all the elements of a pooling region in a sequence and assigns different weights to these elements based upon their orders in the sequence, where the weights are learned via the gr…
This paper presents an investigation of several techniques that increase the accuracy of online handwritten Chinese character recognition (HCCR). We propose a new training strategy named DropDistortion to train a deep convolutional neural network (DCNN) with distorted samples. DropDistortion gradually lowers the degree of character distortion during training, which allows the DCNN to better generalize. Path signature is used to extract effective features for online characters. Further improvement is achieved by employing spatial stochastic max-pooling as a method of feature map distortion and …
School of Electrical and Electronic Engineering（电气与电子工程学院）
Temporal Action Localization (TAL) is a challenging task in video understanding that aims to identify and localize actions within a video sequence. Recent studies have emphasized the importance of applying long-term temporal context modeling (TCM) blocks to the extracted video clip features such as employing complex self-attention mechanisms. In this paper, we present the simplest method ever to address this task and argue that the extracted video clip features are already informative to achieve outstanding performance without sophisticated architectures. To this end, we introduce TemporalMaxe…
IDSIA（达勒·莫勒人工智能研究所）；USI-SUPSI（卢加诺大学-瑞士南部应用科学大学）；Dalle Molle Institute for Artificial Intelligence（达勒·莫勒人工智能研究所）；University of Lugano (USI)（卢加诺大学（USI））；University of Applied Sciences of Southern Switzerland (SUPSI)（瑞士南部应用科学大学（SUPSI））
Deep Neural Networks now excel at image classification, detection and segmentation. When used to scan images by means of a sliding window, however, their high computational complexity can bring even the most powerful hardware to its knees. We show how dynamic programming can speedup the process by orders of magnitude, even when max-pooling layers are present.
Center for Machine Perception（机器感知中心）；FEE CTU Prague（捷克布拉格技术大学电子工程学院）；Irisa Rennes（雷恩信息与随机系统研究所）；Facebook AI Research（脸书人工智能研究院）；Inria（法国国家信息与自动化研究所）
Recently, image representation built upon Convolutional Neural Network (CNN) has been shown to provide effective descriptors for image search, outperforming pre-CNN features as short-vector representations. Yet such models are not compatible with geometry-aware re-ranking methods and still outperformed, on some particular object retrieval benchmarks, by traditional image search systems relying on precise descriptor matching, geometric re-ranking, or query expansion. This work revisits both retrieval stages, namely initial search and re-ranking, by employing the same primitive information deriv…
Deep convolutional networks have recently shown excellent performance on Fine-Grained Vehicle Classification. Based on these existing works, we consider that the back-probation algorithm does not focus on extracting less discriminative feature as much as possible, but focus on that the loss function equals zero. Intuitively, if we can learn less discriminative features, and these features still could fit the training data well, the generalization ability of neural network could be improved. Therefore, we propose a new layer which is placed between fully connected layers and convolutional layer…
We introduce a novel loss max-pooling concept for handling imbalanced training data distributions, applicable as alternative loss layer in the context of deep neural networks for semantic image segmentation. Most real-world semantic segmentation datasets exhibit long tail distributions with few object categories comprising the majority of data and consequently biasing the classifiers towards them. Our method adaptively re-weights the contributions of each pixel based on their observed losses, targeting under-performing classification results as often encountered for under-represented object cl…
Tianjin University of Technology（天津理工大学）；Nanjing University of Information Science and Technology（南京信息工程大学）
Due to its efficiency and stability, Robust Principal Component Analysis (RPCA) has been emerging as a promising tool for moving object detection. Unfortunately, existing RPCA based methods assume static or quasi-static background, and thereby they may have trouble in coping with the background scenes that exhibit a persistent dynamic behavior. In this work, we shall introduce two techniques to fill in the gap. First, instead of using the raw pixel-value as features that are brittle in the presence of dynamic background, we devise a so-called Gaussian max-pooling operator to estimate a "stable…
In convolutional neural network-based character recognition, pooling layers play an important role in dimensionality reduction and deformation compensation. However, their kernel shapes and pooling operations are empirically predetermined; typically, a fixed-size square kernel shape and max pooling operation are used. In this paper, we propose a meta-learning framework for pooling layers. As part of our framework, a parameterized pooling layer is proposed in which the kernel shape and pooling operation are trainable using two parameters, thereby allowing flexible pooling of the input data. We …
Faculty of Mathematics and Computer Science Jagiellonian University（雅盖隆大学数学与计算机科学学院）；Ardigen
Global pooling, such as max- or sum-pooling, is one of the key ingredients in deep neural networks used for processing images, texts, graphs and other types of structured data. Based on the recent DeepSets architecture proposed by Zaheer et al. (NIPS 2017), we introduce a Set Aggregation Network (SAN) as an alternative global pooling layer. In contrast to typical pooling operators, SAN allows to embed a given set of features to a vector representation of arbitrary size. We show that by adjusting the size of embedding, SAN is capable of preserving the whole information from the input. In experi…
Weakly Supervised Semantic Segmentation (WSSS) research has explored many directions to improve the typical pipeline CNN plus class activation maps (CAM) plus refinements, given the image-class label as the only supervision. Though the gap with the fully supervised methods is reduced, further abating the spread seems unlikely within this framework. On the other hand, WSSS methods based on Vision Transformers (ViT) have not yet explored valid alternatives to CAM. ViT features have been shown to retain a scene layout, and object boundaries in self-supervised learning. To confirm these findings, …
University of Montreal（蒙特利尔大学）；Cornell University（康奈尔大学）；Ecole Polytechnique of Montreal（蒙特利尔高等理工学院）；CIFAR（加拿大高等研究院）
Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited; however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform we…
In this paper, we deal with two challenges for measuring the similarity of the subject identities in practical video-based face recognition - the variation of the head pose in uncontrolled environments and the computational expense of processing videos. Since the frame-wise feature mean is unable to characterize the pose diversity among frames, we define and preserve the overall pose diversity and closeness in a video. Then, identity will be the only source of variation across videos since the pose varies even within a single video. Instead of simply using all the frames, we select those faces…
The pooling operation is a cornerstone element of convolutional neural networks. These elements generate receptive fields for neurons, in which local perturbations should have minimal effect on the output activations, increasing robustness and invariance of the network. In this paper we will present an altered version of the most commonly applied method, maximum pooling, where pooling in theory is substituted by a continuous time differential equation, which generates a location sensitive pooling operation, more similar to biological receptive fields. We will present how this continuous method…
