In this work, we explain in detail how receptive fields, effective receptive fields, and projective fields of neurons in different layers, convolution or pooling, of a Convolutional Neural Network (CNN) are calculated. While our focus here is on CNNs, the same operations, but in the reverse order, can be used to calculate these quantities for deconvolutional neural networks. These are important concepts, not only for better understanding and analyzing convolutional and deconvolutional networks, but also for optimizing their performance in real-world applications.
One of the methods used in image recognition is the Deep Convolutional Neural Network (DCNN). DCNN is a model in which the expressive power of features is greatly improved by deepening the hidden layer of CNN. The architecture of CNNs is determined based on a model of the visual cortex of mammals. There is a model called Residual Network (ResNet) that has a skip connection. ResNet is an advanced model in terms of the learning method, but it has not been interpreted from a biological viewpoint. In this research, we investigate the receptive fields of a ResNet on the classification task in Image…
University of California, San Diego（加利福尼亚大学圣地亚哥分校）
In this work, we present the depth-adaptive deep neural network using a depth map for semantic segmentation. Typical deep neural networks receive inputs at the predetermined locations regardless of the distance from the camera. This fixed receptive field presents a challenge to generalize the features of objects at various distances in neural networks. Specifically, the predetermined receptive fields are too small at a short distance, and vice versa. To overcome this challenge, we develop a neural network which is able to adapt the receptive field not only for each layer but also for each neur…
PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, and Jiangsu Key Lab of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；Momenta；National Key Lab for Novel Software Technology, Nanjing University（南京大学）；Tsinghua National Laboratory for Information Science and Technology (TNList) Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
In standard Convolutional Neural Networks (CNNs), the receptive fields of artificial neurons in each layer are designed to share the same size. It is well-known in the neuroscience community that the receptive field size of visual cortical neurons are modulated by the stimulus, which has been rarely considered in constructing CNNs. We propose a dynamic selection mechanism in CNNs that allows each neuron to adaptively adjust its receptive field size based on multiple scales of input information. A building block called Selective Kernel (SK) unit is designed, in which multiple branches with diff…
Visual perception results from a systematic transformation of the information flowing through the visual system. In the neuronal hierarchy, the response properties of single neurons are determined by neurons located one level below, and in turn, determine the responses of neurons located one level above. Therefore in modeling receptive fields, it is essential to ensure that the response properties of neurons in a given level can be generated by combining the response models of neurons in its input levels. However, existing response models of neurons in the motion cortex do not inherently yield…
Quantum Lucid Research Laboratories（Quantum Lucid研究实验室）；Howard University Hospital（霍华德大学医院）
Our visual system is astonishingly efficient at detecting moving objects. This process is mediated by the neurons which connect the primary visual cortex (V1) to the middle temporal (MT) area. Interestingly, since Kuffler's pioneering experiments on retinal ganglion cells, mathematical models have been vital for advancing our understanding of the receptive fields of visual neurons. However, existing models were not designed to describe the most salient attributes of the highly specialized neurons in the V1 to MT motion processing stream; and they have not been able to do so. Here, we introduce…
Qatar University（卡塔尔大学）；Tampere University（坦佩雷大学）；Huawei Technologies Oy (Finland)（华为技术有限公司（芬兰））；Izmir University of Economics（伊兹密尔经济大学）；Microsoft (Finland)（微软（芬兰））
University of Maryland, College Park, MD USA（马里兰大学帕克分校）；Nanjing University, Nanjing, China（南京大学）
Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressive moving-average (ARMA) layer, a novel module with an adjustable receptive field controlled by the learnable autoregressive coefficients. Compared with traditional convoluti…
Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can dramatically change a network's output prediction. In contrast to what is known from biology, these networks largely rely on feedforward connections, ignoring the influence of recurrent connections. They also focus on supervised rather than unsupervised learning. To address these issues, we combine traditional supervised learning via backpropagation with a spe…
University of Colorado School of Medicine（科罗拉多大学医学院）；Canadian Institute for Advanced Research（加拿大高等研究院）
Primary visual cortex (V1) is the first stage of cortical image processing, and a major effort in systems neuroscience is devoted to understanding how it encodes information about visual stimuli. Within V1, many neurons respond selectively to edges of a given preferred orientation: these are known as simple or complex cells, and they are well-studied. Other neurons respond to localized center-surround image features. Still others respond selectively to certain image stimuli, but the specific features that excite them are unknown. Moreover, even for the simple and complex cells-- the best-under…
Classical image denoising methods utilize the non-local self-similarity principle to effectively recover image content from noisy images. Current state-of-the-art methods use deep convolutional neural networks (CNNs) to effectively learn the mapping from noisy to clean images. Deep denoising CNNs manifest a high learning capacity and integrate non-local information owing to the large receptive field yielded by numerous cascade of hidden layers. However, deep networks are also computationally complex and require large data for training. To address these issues, this study draws the focus on the…
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…
Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University（上海大学特种光纤与光接入网重点实验室）；Department of Computer Science, Johns Hopkins University（约翰斯·霍普金斯大学计算机科学系）
In the field of connectomics, neuroscientists seek to identify cortical connectivity comprehensively. Neuronal boundary detection from the Electron Microscopy (EM) images is often done to assist the automatic reconstruction of neuronal circuit. But the segmentation of EM images is a challenging problem, as it requires the detector to be able to detect both filament-like thin and blob-like thick membrane, while suppressing the ambiguous intracellular structure. In this paper, we propose multi-stage multi-recursive-input fully convolutional networks to address this problem. The multiple recursiv…
Institute of Automation, CAS（中国科学院自动化研究所）；School of Artificial Intelligence, UCAS（中国科学院大学人工智能学院）；Youtu Lab, Tencent（腾讯优图实验室）；CASIA-LLVision Joint Lab（中国科学院自动化研究所-联汇视界联合实验室）；Y-Tech, Kuaishou Technology（快手科技Y-Tech）
Object detection has achieved remarkable progress in the past decade. However, the detection of oriented and densely packed objects remains challenging because of following inherent reasons: (1) receptive fields of neurons are all axis-aligned and of the same shape, whereas objects are usually of diverse shapes and align along various directions; (2) detection models are typically trained with generic knowledge and may not generalize well to handle specific objects at test time; (3) the limited dataset hinders the development on this task. To resolve the first two issues, we present a dynamic …
University of Oxford（牛津大学）；Tsinghua University（清华大学）
The convolutional neural network (CNN) has become a basic model for solving many computer vision problems. In recent years, a new class of CNNs, recurrent convolution neural network (RCNN), inspired by abundant recurrent connections in the visual systems of animals, was proposed. The critical element of RCNN is the recurrent convolutional layer (RCL), which incorporates recurrent connections between neurons in the standard convolutional layer. With increasing number of recurrent computations, the receptive fields (RFs) of neurons in RCL expand unboundedly, which is inconsistent with biological…
University of Exeter（埃克塞特大学）；Department of Computer Science, College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK（埃克塞特大学工程、数学与物理科学学院计算机科学系（注：此处按要求提取到大学级别，故主要机构为University of Exeter））
Deep convolutional neural networks have achieved impressive performance on a broad range of problems, beating prior art on established benchmarks, but it often remains unclear what are the representations learnt by those systems and how they achieve such performance. This article examines the specific problem of saliency detection, where benchmarks are currently dominated by CNN-based approaches, and investigates the properties of the learnt representation by visualizing the artificial neurons' receptive fields. We demonstrate that fine tuning a pre-trained network on the saliency detection ta…
Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields
Computational Brain Science Lab（计算脑科学实验室）；Division of Computational Science and Technology（计算科学与技术系）；KTH Royal Institute of Technology（皇家理工学院）
The human visual system has a hierarchical structure consisting of layers of processing, such as the retina, V1, V2, etc. Understanding the functional roles of these visual processing layers would help to integrate the psychophysiological and neurophysiological models into a consistent theory of human vision, and would also provide insights to computer vision research. One classical theory of the early visual pathway hypothesizes that it serves to capture the statistical structure of the visual inputs by efficiently coding the visual information in its outputs. Until recently, most computation…
Facebook（脸书）；Google（谷歌）；The University of Hong Kong（香港大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carnegie Mellon University（卡内基梅隆大学）
State-of-the-art results of semantic segmentation are established by Fully Convolutional neural Networks (FCNs). FCNs rely on cascaded convolutional and pooling layers to gradually enlarge the receptive fields of neurons, resulting in an indirect way of modeling the distant contextual dependence. In this work, we advocate the use of spatially recurrent layers (i.e. ReNet layers) which directly capture global contexts and lead to improved feature representations. We demonstrate the effectiveness of ReNet layers by building a Naive deep ReNet (N-ReNet), which achieves competitive performance on …
University of California, Santa Barbara（加州大学圣巴巴拉分校）；Massachusetts Institute of Technology（麻省理工学院）；Université de Toulouse（图卢兹大学）
Deep neural networks have surpassed human performance in key visual challenges such as object recognition, but require a large amount of energy, computation, and memory. In contrast, spiking neural networks (SNNs) have the potential to improve both the efficiency and biological plausibility of object recognition systems. Here we present a SNN model that uses spike-latency coding and winner-take-all inhibition (WTA-I) to efficiently represent visual stimuli from the Fashion MNIST dataset. Stimuli were preprocessed with center-surround receptive fields and then fed to a layer of spiking neurons …
Institute for Theoretical Computer Science, Graz University of Technology（格拉茨技术大学理论计算机科学研究所）
Deep convolutional neural networks (CNNs) have demonstrated impressive performance on visual object classification tasks. In addition, it is a useful model for predication of neuronal responses recorded in visual system. However, there is still no clear understanding of what CNNs learn in terms of visual neuronal circuits. Visualizing CNN's features to obtain possible connections to neuronscience underpinnings is not easy due to highly complex circuits from the retina to higher visual cortex. Here we address this issue by focusing on single retinal ganglion cells with a simple model and electr…
A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple a tool, the translation-sensitivity map, which we use to visualize and quantify the translation-invaria…
IDSIA（达勒·莫勒人工智能研究所）；University of Lugano（卢加诺大学）；University of Applied Sciences of Southern Switzerland（瑞士南部应用科学大学）
Traditional methods of computer vision and machine learning cannot match human performance on tasks such as the recognition of handwritten digits or traffic signs. Our biologically plausible deep artificial neural network architectures can. Small (often minimal) receptive fields of convolutional winner-take-all neurons yield large network depth, resulting in roughly as many sparsely connected neural layers as found in mammals between retina and visual cortex. Only winner neurons are trained. Several deep neural columns become experts on inputs preprocessed in different ways; their predictions …
We propose contextual convolution (CoConv) for visual recognition. CoConv is a direct replacement of the standard convolution, which is the core component of convolutional neural networks. CoConv is implicitly equipped with the capability of incorporating contextual information while maintaining a similar number of parameters and computational cost compared to the standard convolution. CoConv is inspired by neuroscience studies indicating that (i) neurons, even from the primary visual cortex (V1 area), are involved in detection of contextual cues and that (ii) the activity of a visual neuron c…
Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息创新研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Suzhou Research Institute, Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息创新研究院苏州研究院）
At present, the Synthetic Aperture Radar (SAR) image classification method based on convolution neural network (CNN) has faced some problems such as poor noise resistance and generalization ability. Spiking neural network (SNN) is one of the core components of brain-like intelligence and has good application prospects. This article constructs a complete SAR image classifier based on unsupervised and supervised learning of SNN by using spike sequences with complex spatio-temporal information. We firstly expound the spiking neuron model, the receptive field of SNN, and the construction of spike …
Both neurophysiological and psychophysical experiments have pointed out the crucial role of recurrent and feedback connections to process context-dependent information in the early visual cortex. While numerous models have accounted for feedback effects at either neural or representational level, none of them were able to bind those two levels of analysis. Is it possible to describe feedback effects at both levels using the same model? We answer this question by combining Predictive Coding (PC) and Sparse Coding (SC) into a hierarchical and convolutional framework. In this Sparse Deep Predicti…
Hyperspectral imagery is rich in spatial and spectral information. Using 3D-CNN can simultaneously acquire features of spatial and spectral dimensions to facilitate classification of features, but hyperspectral image information spectral dimensional information redundancy. The use of continuous 3D-CNN will result in a high amount of parameters, and the computational power requirements of the device are high, and the training takes too long. This letter designed the Faster selective kernel mechanism network (FSKNet), FSKNet can balance this problem. It designs 3D-CNN and 2D-CNN conversion modul…
Traveling Waves Integrate Spatial Information Through Time
The Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University（凯普纳人工智能自然研究 institute，哈佛大学）；Western University, Department of Mathematics, London, Ontario, Canada（西方大学，数学系，伦敦，安大略，加拿大）
Central China Normal University（华中师范大学）；Hubei University of Technology（湖北工业大学）
Deep Learning (DL) based Compressed Sensing (CS) has been applied for better performance of image reconstruction than traditional CS methods. However, most existing DL methods utilize the block-by-block measurement and each measurement block is restored separately, which introduces harmful blocking effects for reconstruction. Furthermore, the neuronal receptive fields of those methods are designed to be the same size in each layer, which can only collect single-scale spatial information and has a negative impact on the reconstruction process. This paper proposes a novel framework named Multi-s…
Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and has outperformed the traditional non-local class of methods. However, the top-performing networks are generally composed of many convolutional layers and hundreds of neurons, with trainable parameters in excess of several millions. We claim that this is due to the inherent linear nature of convolution-based transformation, which is inadequate for handling seve…
