Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional neural networks applied to approximate functions on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$. Our analysis presents rates of uniform approximation when the approximated function lies in the Sobolev space $W^r_\infty (\mathbb{S}^{d-1})$ with $r>0$ or takes an additive ridge form. Our work verifies theoretically the modelling and approximation ability of deep convolutional neural networks followed by downsampling and one fully connected layer or two. The key idea of our spherical analysis is to use the inner product form of the reproducing kernels of the spaces of spherical harmonics and then to apply convolutional factorizations of filters to realize the generated linear features.
In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a novel area-regular hierarchical partition on the 2-sphere and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrating the effectiveness of our area-regular spherical Haar tight framelets in several denoising experiments. Furthermore, we propose a convolutional neural network (CNN) model for spherical signal denoising which employs the fast framelet d…
The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and egineering deal with signals with other symmetries, such as rotation invariant data on the sphere. Examples include climate and weather science, astrophysics, and chemistry. In this paper we present spherical convolutional networks. These networks use convolutions on the sphere and rotation group, which results in rotational weight sharing and rotation equivarianc…
The University of Chicago（芝加哥大学）；Toyota Technological Institute（丰田工业研究所）
Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the…
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）
Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others. This paper investigates the properties that Spherical CNNs exhibit as they pertain to the rotational structure inherent in spherical signals. We build upon the rotation equivariance of spherical convolutions to show that Spherical CNNs are stable to general structure perturbations. In particular, we model arbitrary structure perturbations as diffeomorphism …
Spherical convolutional neural networks can improve brain microstructure estimation from diffusion MRI data
UCL Great Ormond Street Institute of Child Health, University College London（伦敦大学学院大奥蒙德街儿童健康研究所）；Great Ormond Street Hospital（大奥蒙德街医院）；Lund University（隆德大学）
University of Amsterdam（阿姆斯特丹大学）；EPFL（洛桑联邦理工学院）；CIFAR（加拿大高等研究院）
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational w…
UC Irvine（加州大学欧文分校）；University of Edinburgh（爱丁堡大学）；Ecole Polytechnique de Montreal（蒙特利尔理工学院）；University of Alberta（阿尔伯塔大学）；University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Yes, they do. This paper provides the first empirical demonstration that deep convolutional models really need to be both deep and convolutional, even when trained with methods such as distillation that allow small or shallow models of high accuracy to be trained. Although previous research showed that shallow feed-forward nets sometimes can learn the complex functions previously learned by deep nets while using the same number of parameters as the deep models they mimic, in this paper we demonstrate that the same methods cannot be used to train accurate models on CIFAR-10 unless the student m…
CREST, ENSAE（CREST，ENSAE）；University of Washington（华盛顿大学）
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network expands into a sum involving elementary functions akin to spherical harmonics. This functional decomposition can be related to the functional ANOVA decomposition in nonparametric statistics. Building off our functional characterization of convolutional networks, we obtain statistical bounds highlighting an interesting trade-off between the approximation error and…
We describe convolutional deep exponential families (CDEFs) in this paper. CDEFs are built based on deep exponential families, deep probabilistic models that capture the hierarchical dependence between latent variables. CDEFs greatly reduce the number of free parameters by tying the weights of DEFs. Our experiments show that CDEFs are able to uncover time correlations with a small amount of data.
Aalto university（阿尔托大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image classification. We demonstrate greatly improved image classification performance compared to current Gaussian process approaches on the MNIST and CIFAR-10 datasets. In particular, we improve CIFAR-10 accuracy by over 10 percentage points.
In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper. Convolutional dictionaries are more suitable for processing high-dimensional signals like for example images and have only a small number of free parameters. By exploiting the properties of a convolutional dictionary, we present an efficient convolutional analysis dictionary learning approach. A L-layer DeepCAM consists of L layers of convolutional anal…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks having convolutional structures. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approxim…
This paper describes our UNet based deep convolutional neural network approach on the Traffic4cast challenge 2019. Challenges task is to predict future traffic flow volume, heading and speed on high resolution whole city map. We used UNet based deep convolutional neural network to train predictive model for the short term traffic forecast. On each convolution block, layers are densely connected with subsequent layers like a DenseNet. Trained and evaluated on the real world data set collected from three distinct cities in the world, our method achieved best performance in this challenge.
Swiss Data Science Center (SDSC)（瑞士数据科学中心）；EPFL（洛桑联邦理工学院）；ETH Zurich（苏黎世联邦理工学院）
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We pr…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty estimates and a marginal likelihood objective, but their weak inductive biases lead to inferior accuracy. This has limited their applicability in certain tasks (e.g. image classification). We propose a translation-insensitive convolutional kernel, which relaxes the translation invariance constraint imposed by previous convolutional GPs. We show how we can use t…
Indraprastha Institute of Information Technology Delhi（德里英迪拉普拉斯信息技术学院）；Inria Saclay（法国国家信息与自动化研究所萨克雷分院）；Univ. Paris-Saclay（巴黎萨克雷大学）；CentraleSupélec（中央理工-高等电力学院）；LIGM（巴黎东部克雷泰伊大学计算机科学实验室）；ESIEE Paris（巴黎高等电子与电工技术工程师学院）；Univ. Gustave Eiffel（古斯塔夫·埃菲尔大学）
This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different layers. The features extracted in an unsupervised manner can then be used to perform machine learning tasks, such as classification and clustering. The learning technique relies on a well-sounded alternating proximal minimization scheme with established convergence guarantees. Our experimental results show that the proposed DCTL technique outperforms its shallo…
A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images, and excellent classification results are obtained on the MNIST and Caltech 101 datasets.
Renmin University of China（中国人民大学）；Fudan University（复旦大学）；Alibaba Group（阿里巴巴集团）
Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theor…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.
University of California, Riverside（加州大学河滨分校）；University of Southern California（南加利福尼亚大学）
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed Deep Tensor Decomposition (DeepTD) is based on a rank-1 tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to …
Traditional vision-based hand gesture recognition systems is limited under dark circumstances. In this paper, we build a hand gesture recognition system based on microwave transceiver and deep learning algorithm. A Doppler radar sensor with dual receiving channels at 5.8GHz is used to acquire a big database of hand gestures signals. The received hand gesture signals are then processed with time-frequency analysis. Based on these big databases of hand gesture, we propose a new machine learning architecture called deformable deep convolutional generative adversarial network. Experimental results…
Amity Institute of Information Technology（阿米提信息技术学院）；Amity University（阿米提大学）；Coventry University（考文垂大学）
In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep clustering framework and compared with the possible classical implementation. Our investigation shows that the proposed quantum version of deep clustering formulation demonstrates a significant performance gain (exponential speed up gains in many sections) against the possible cla…
Peking University（北京大学）；Beijing Institute of Big Data Research（北京大数据研究院）
Timely accurate traffic forecast is crucial for urban traffic control and guidance. Due to the high nonlinearity and complexity of traffic flow, traditional methods cannot satisfy the requirements of mid-and-long term prediction tasks and often neglect spatial and temporal dependencies. In this paper, we propose a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain. Instead of applying regular convolutional and recurrent units, we formulate the problem on graphs and build the model with complete con…
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on co…
This study attempts to analyze patterns in cryptocurrency markets using a special type of deep neural networks, namely a convolutional autoencoder. The method extracts the dominant features of market behavior and classifies the 40 studied cryptocurrencies into several classes for twelve 6-month periods starting from 15th May 2013. Transitions from one class to another with time are related to the maturement of cryptocurrencies. In speculative cryptocurrency markets, these findings have potential implications for investment and trading strategies.
MILA, Université de Montréal（蒙特利尔大学 MILA）；AIRLab, Politecnico di Milano（米兰理工大学 AIRLab）
We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers, as well as the relationship between convolutional and transposed convolutional layers. Relationships are derived for various cases, and are illustrated in order to make them intuitive.
Bar-Ilan University（巴伊兰大学）；University of Maryland（马里兰大学）
In this paper we describe the problem of painter classification, and propose a novel approach based on deep convolutional autoencoder neural networks. While previous approaches relied on image processing and manual feature extraction from paintings, our approach operates on the raw pixel level, without any preprocessing or manual feature extraction. We first train a deep convolutional autoencoder on a dataset of paintings, and subsequently use it to initialize a supervised convolutional neural network for the classification phase. The proposed approach substantially outperforms previous method…
DELIMIT is a framework extension for deep learning in diffusion imaging, which extends the basic framework PyTorch towards spherical signals. Based on several novel layers, deep learning can be applied to spherical diffusion imaging data in a very convenient way. First, two spherical harmonic interpolation layers are added to the extension, which allow to transform the signal from spherical surface space into the spherical harmonic space, and vice versa. In addition, a local spherical convolution layer is introduced that adds the possibility to include gradient neighborhood information within …
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Massachusetts Institute of Technology（麻省理工学院）
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and $SO(3)$ convolutions, researchers have recently developed deep learning methods better suited for classifying spherical images. These newly proposed convolutional layers naturally extend the notion of convolution to functions on the unit sphere $S^2$ and the group of rotations $SO(3)$ and these layers are equivariant to 3D rotations. In this paper, we consider th…
China University of Political Science and Law（中国政法大学）；Institute of High Performance Computing（高性能计算研究所）
A deep learning approach has been widely applied in sequence modeling problems. In terms of automatic speech recognition (ASR), its performance has significantly been improved by increasing large speech corpus and deeper neural network. Especially, recurrent neural network and deep convolutional neural network have been applied in ASR successfully. Given the arising problem of training speed, we build a novel deep recurrent convolutional network for acoustic modeling and then apply deep residual learning to it. Our experiments show that it has not only faster convergence speed but better recog…
Convolutional deep sets are the architecture of a deep neural network (DNN) that can model stationary stochastic process. This architecture uses the kernel smoother and the DNN to construct the translation equivariant functional representations, and thus reflects the inductive bias of the stationarity into DNN. However, since this architecture employs the kernel smoother known as the non-parametric model, it may produce ambiguous representations when the number of data points is not given sufficiently. To remedy this issue, we introduce Bayesian convolutional deep sets that construct the rando…
Deep Convolutional Networks (DCNs) have been shown to be sensitive to Universal Adversarial Perturbations (UAPs): input-agnostic perturbations that fool a model on large portions of a dataset. These UAPs exhibit interesting visual patterns, but this phenomena is, as yet, poorly understood. Our work shows that visually similar procedural noise patterns also act as UAPs. In particular, we demonstrate that different DCN architectures are sensitive to Gabor noise patterns. This behaviour, its causes, and implications deserve further in-depth study.
Learning from data in the quaternion domain enables us to exploit internal dependencies of 4D signals and treating them as a single entity. One of the models that perfectly suits with quaternion-valued data processing is represented by 3D acoustic signals in their spherical harmonics decomposition. In this paper, we address the problem of localizing and detecting sound events in the spatial sound field by using quaternion-valued data processing. In particular, we consider the spherical harmonic components of the signals captured by a first-order ambisonic microphone and process them by using a…
Rice University（莱斯大学）；Prudence Medical Technologies Ltd（审慎医疗技术有限公司）
We train an enhanced deep convolutional neural network in order to identify eight cardiac abnormalities from the standard 12-lead electrocardiograms (ECGs) using the dataset of 14000 ECGs. Instead of straightforwardly applying an end-to-end deep learning approach, we find that deep convolutional neural networks enhanced with sophisticated hand crafted features show advantages in reducing generalization errors. Additionally, data preprocessing and augmentation are essential since the distribution of eight cardiac abnormalities are highly biased in the given dataset. Our approach achieves promis…
Deep convolutional neural networks comprise a subclass of deep neural networks (DNN) with a constrained architecture that leverages the spatial and temporal structure of the domain they model. Convolutional networks achieve the best predictive performance in areas such as speech and image recognition by hierarchically composing simple local features into complex models. Although DNNs have been used in drug discovery for QSAR and ligand-based bioactivity predictions, none of these models have benefited from this powerful convolutional architecture. This paper introduces AtomNet, the first struc…
Auburn University（奥本大学）；Verizon Media Group (Yahoo!)（威瑞森媒体集团（雅虎））；Amazon.com Inc.（亚马逊公司）
We have proposed to develop a global hybrid deep learning framework to predict the daily prices in the stock market. With representation learning, we derived an embedding called Stock2Vec, which gives us insight for the relationship among different stocks, while the temporal convolutional layers are used for automatically capturing effective temporal patterns both within and across series. Evaluated on S&P 500, our hybrid framework integrates both advantages and achieves better performance on the stock price prediction task than several popular benchmarked models.
We introduce a new deep convolutional neural network, CrescendoNet, by stacking simple building blocks without residual connections. Each Crescendo block contains independent convolution paths with increased depths. The numbers of convolution layers and parameters are only increased linearly in Crescendo blocks. In experiments, CrescendoNet with only 15 layers outperforms almost all networks without residual connections on benchmark datasets, CIFAR10, CIFAR100, and SVHN. Given sufficient amount of data as in SVHN dataset, CrescendoNet with 15 layers and 4.1M parameters can match the performanc…
Obesity is an important concern in public health, and Body Mass Index is one of the useful (and proliferant) measures. We use Convolutional Neural Networks to determine Body Mass Index from photographs in a study with 161 participants. Low data, a common problem in medicine, is addressed by reducing the information in the photographs by generating silhouette images. Results present with high correlation when tested on unseen data.
We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentati…
RJ Research Consulting（RJ研究咨询公司）；Rutgers University（罗格斯大学）
This paper reports the performances of shallow word-level convolutional neural networks (CNN), our earlier work (2015), on the eight datasets with relatively large training data that were used for testing the very deep character-level CNN in Conneau et al. (2016). Our findings are as follows. The shallow word-level CNNs achieve better error rates than the error rates reported in Conneau et al., though the results should be interpreted with some consideration due to the unique pre-processing of Conneau et al. The shallow word-level CNN uses more parameters and therefore requires more storage th…
Thayer School of Engineering（塞耶工程学院）；Dartmouth College（达特茅斯学院）
In this paper, we present a system that employs a wearable acoustic sensor and a deep convolutional neural network for detecting coughs. We evaluate the performance of our system on 14 healthy volunteers and compare it to that of other cough detection systems that have been reported in the literature. Experimental results show that our system achieves a classification sensitivity of 95.1% and a specificity of 99.5%.
Old Dominion University（欧道明大学）；Sun Yat-sen University（中山大学）
Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a fixed width. This does not cover the important convolutional neural networks where the widths are increasing from layer to layer. For this reason, we first study convergence of general ReLU networks with increasing widths and then apply the results obtained to deep convolutional neural networks. It turns out the convergence reduces to convergence of infinite p…
University of Toronto（多伦多大学）；Toronto Rehabilitation Institute（多伦多康复研究所）；University Health Network（大学健康网络）
Human falls rarely occur; however, detecting falls is very important from the health and safety perspective. Due to the rarity of falls, it is difficult to employ supervised classification techniques to detect them. Moreover, in these highly skewed situations it is also difficult to extract domain specific features to identify falls. In this paper, we present a novel framework, \textit{DeepFall}, which formulates the fall detection problem as an anomaly detection problem. The \textit{DeepFall} framework presents the novel use of deep spatio-temporal convolutional autoencoders to learn spatial …
In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit an implicit tendency towards low matrix and tensor ranks, respectively. Drawing closer to practical deep learning, the current paper theoretically analyzes the implicit regularization in hierarchical tensor factorization, a model equivalent to certain deep convolutional neural networks. Through a dynamical systems lens, we overcome challenges associated with hierarchy, and est…
We prove bounds on the generalization error of convolutional networks. The bounds are in terms of the training loss, the number of parameters, the Lipschitz constant of the loss and the distance from the weights to the initial weights. They are independent of the number of pixels in the input, and the height and width of hidden feature maps. We present experiments using CIFAR-10 with varying hyperparameters of a deep convolutional network, comparing our bounds with practical generalization gaps.
Xi’an Jiaotong University（西安交通大学）；City University of Hong Kong（香港城市大学）
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove that implementing empirical risk minimization on DCNNs with expansive convolution (with zero-padding) is strongly universally consistent. Motivated by the universal consistency, we conduct a series of experiments to show that without any fully connected layers, DCNNs with expansive convolution perform not worse than the widely used deep neural net…
Indraprastha Institute of Information Technology, Delhi（德里英德拉普拉斯塔信息技术学院）；TCS Research（塔塔咨询服务研究院）；Université Paris-Saclay（巴黎-萨克雷大学）；CentraleSupélec（高等电力学院）；Inria（法国国家信息与自动化研究所）；LIGM（LIGM实验室）；Université Gustave Eiffel（古斯塔夫·埃菲尔大学）；CNRS（法国国家科学研究中心）；ESIEE Paris（巴黎高等电子工程师学院）
This work proposes an unsupervised fusion framework based on deep convolutional transform learning. The great learning ability of convolutional filters for data analysis is well acknowledged. The success of convolutive features owes to convolutional neural network (CNN). However, CNN cannot perform learning tasks in an unsupervised fashion. In a recent work, we show that such shortcoming can be addressed by adopting a convolutional transform learning (CTL) approach, where convolutional filters are learnt in an unsupervised fashion. The present paper aims at (i) proposing a deep version of CTL;…
Center for Brains, Minds and Machines（脑、心智与机器中心）；Massachusetts Institute of Technology（麻省理工学院）
The main success stories of deep learning, starting with ImageNet, depend on deep convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines, and also better than deep fully connected networks; but what is so special about deep convolutional networks? Recent results in approximation theory proved an exponential advantage of deep convolutional networks with or without shared weights in approximating functions with hierarchical locality in their compositional structure. More recently, the hierarchical structur…
The development of a deep (stacked) convolutional auto-encoder in the Caffe deep learning framework is presented in this paper. We describe simple principles which we used to create this model in Caffe. The proposed model of convolutional auto-encoder does not have pooling/unpooling layers yet. The results of our experimental research show comparable accuracy of dimensionality reduction in comparison with a classic auto-encoder on the example of MNIST dataset.
NCSA（美国国家超级计算应用中心）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We discuss the development of novel deep learning algorithms to enable real-time regression analysis for time series data. We showcase the application of this new method with a timely case study, and then discuss the applicability of this approach to tackle similar challenges across science domains.
Institute for Artificial Intelligence at Tsinghua University（清华大学人工智能研究院）；State Key Laboratory of Intelligent Technology and Systems（智能技术与系统国家重点实验室）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Center for Intelligent Connected Vehicles and Transportation（智能网联汽车与运输中心）；Department of Computer Science, Tsinghua University（清华大学计算机系）
Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious over-smoothing at the same time. Considering that the wavelet transform generally has a stronger ability to extract useful information than the Fourier transform, we propose a new deep graph wavelet convolutional network (DeepGWC) for semi-supervised node classification tasks. Based on the optimized static filtering matrix parameters of vanilla graph wavelet neural …
We propose an image super-resolution method (SR) using a deeply-recursive convolutional network (DRCN). Our network has a very deep recursive layer (up to 16 recursions). Increasing recursion depth can improve performance without introducing new parameters for additional convolutions. Albeit advantages, learning a DRCN is very hard with a standard gradient descent method due to exploding/vanishing gradients. To ease the difficulty of training, we propose two extensions: recursive-supervision and skip-connection. Our method outperforms previous methods by a large margin.
Shenzhen Polytechnic（深圳职业技术学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Convolutional neural networks have shown impressive abilities in many applications, especially those related to the classification tasks. However, for the regression problem, the abilities of convolutional structures have not been fully understood, and further investigation is needed. In this paper, we consider the mean squared error analysis for deep convolutional neural networks. We show that, for additive ridge functions, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal mini-max rates (up to a log factor). The input dimensi…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）
The article describes a system for image recognition using deep convolutional neural networks. Modified network architecture is proposed that focuses on improving convergence and reducing training complexity. The filters in the first layer of the network are constrained to fit the Gabor function. The parameters of Gabor functions are learnable and are updated by standard backpropagation techniques. The system was implemented on Python, tested on several datasets and outperformed the common convolutional networks.
We give a formal procedure for computing preimages of convolutional network outputs using the dual basis defined from the set of hyperplanes associated with the layers of the network. We point out the special symmetry associated with arrangements of hyperplanes of convolutional networks that take the form of regular multidimensional polyhedral cones. We discuss the efficiency of large number of layers of nested cones that result from incremental small size convolutions in order to give a good compromise between efficient contraction of data to low dimensions and shaping of preimage manifolds. …
