Most of existing statistical theories on deep neural networks have sample complexities cursed by the data dimension and therefore cannot well explain the empirical success of deep learning on high-dimensional data. To bridge this gap, we propose to exploit low-dimensional geometric structures of the real world data sets. We establish theoretical guarantees of convolutional residual networks (ConvResNet) in terms of function approximation and statistical estimation for binary classification. Specifically, given the data lying on a $d$-dimensional manifold isometrically embedded in $\mathbb{R}^D$, we prove that if the network architecture is properly chosen, ConvResNets can (1) approximate Besov functions on manifolds with arbitrary accuracy, and (2) learn a classifier by minimizing the empirical logistic risk, which gives an excess risk in the order of $n^{-\frac{s}{2s+2(s\vee d)}}$, where $s$ is a smoothness parameter. This implies that the sample complexity depends on the intrinsic dimension $d$, instead of the data dimension $D$. Our results demonstrate that ConvResNets are adaptive to low-dimensional structures of data sets.
Ensemble methods, traditionally built with independently trained de-correlated models, have proven to be efficient methods for reducing the remaining residual generalization error, which results in robust and accurate methods for real-world applications. In the context of deep learning, however, training an ensemble of deep networks is costly and generates high redundancy which is inefficient. In this paper, we present experiments on Ensembles with Shared Representations (ESRs) based on convolutional networks to demonstrate, quantitatively and qualitatively, their data processing efficiency an…
Ben Gurion University（本·古里安大学）；Emory University（埃默里大学）；University of British Columbia（不列颠哥伦比亚大学）；Xtract AI
Convolutional Neural Networks (CNNs) filter the input data using spatial convolution operators with compact stencils. Commonly, the convolution operators couple features from all channels, which leads to immense computational cost in the training of and prediction with CNNs. To improve the efficiency of CNNs, we introduce lean convolution operators that reduce the number of parameters and computational complexity, and can be used in a wide range of existing CNNs. Here, we exemplify their use in residual networks (ResNets), which have been very reliable for a few years now and analyzed intensiv…
Predicting diagnoses from Electronic Health Records (EHRs) is an important medical application of multi-label learning. We propose a convolutional residual model for multi-label classification from doctor notes in EHR data. A given patient may have multiple diagnoses, and therefore multi-label learning is required. We employ a Convolutional Neural Network (CNN) to encode plain text into a fixed-length sentence embedding vector. Since diagnoses are typically correlated, a deep residual network is employed on top of the CNN encoder, to capture label (diagnosis) dependencies and incorporate infor…
Hong Kong Baptist University（香港浸会大学）；Georgia Tech（佐治亚理工学院）；The Hong Kong University of Science and Technology（香港科技大学）；Google Research（谷歌研究院）
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate …
Networks with large receptive field (RF) have shown advanced fitting ability in recent years. In this work, we utilize the short-term residual learning method to improve the performance and robustness of networks for image denoising tasks. Here, we choose a multi-wavelet convolutional neural network (MWCNN), one of the state-of-art networks with large RF, as the backbone, and insert residual dense blocks (RDBs) in its each layer. We call this scheme multi-wavelet residual dense convolutional neural network (MWRDCNN). Compared with other RDB-based networks, it can extract more features of the o…
University of Chinese Academy of Sciences（中国科学院大学）
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Here, we think three factors in each layer of it including the initialization, the dictionary design and the number of iterations greatly affect the performance of ML-CSC. Inspired by these considerations, we propose two novel multi-layer models--residual convolutional spars…
Earthquake signal detection is at the core of observational seismology. A good detection algorithm should be sensitive to small and weak events with a variety of waveform shapes, robust to background noise and non-earthquake signals, and efficient for processing large data volumes. Here, we introduce the Cnn-Rnn Earthquake Detector (CRED), a detector based on deep neural networks. The network uses a combination of convolutional layers and bi-directional long-short-term memory units in a residual structure. It learns the time-frequency characteristics of the dominant phases in an earthquake sig…
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…
Center for Informatics and Computational Science, University of Notre Dame（圣母大学信息与计算科学中心）；Key Laboratory of Surficial Geochemistry of Ministry of Education, School of Earth Sciences and Engineering, Nanjing University（南京大学地球科学与工程学院、表生地球化学教育部重点实验室）
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In this study, we develop a convolutional adversarial autoencoder (CAAE) to parameterize non-Gaussian conductivity fields with heterogeneous conductivity within each facies using a low-dimensional latent representation. In addition, a deep residual dense convolutional network (DRDC…
Due to the success of residual networks (resnets) and related architectures, shortcut connections have quickly become standard tools for building convolutional neural networks. The explanations in the literature for the apparent effectiveness of shortcuts are varied and often contradictory. We hypothesize that shortcuts work primarily because they act as linear counterparts to nonlinear layers. We test this hypothesis by using several variations on the standard residual block, with different types of linear connections, to build small image classification networks. Our experiments show that ot…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Seoul National University Bundang Hospital（首尔国立大学盆唐医院）
Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were not fully recovered. To address this problem, here we propose a novel framelet-based denoising algorithm using wavelet residual network which synergistically combines the expressive power of deep learning and the performance guarantee from the framelet-based denoising algorithms. …
Hefei University of Technology（合肥工业大学）；University of Science and Technology of China（中国科学技术大学）
Graph Convolutional Networks (GCNs) are state-of-the-art graph based representation learning models by iteratively stacking multiple layers of convolution aggregation operations and non-linear activation operations. Recently, in Collaborative Filtering (CF) based Recommender Systems (RS), by treating the user-item interaction behavior as a bipartite graph, some researchers model higher-layer collaborative signals with GCNs. These GCN based recommender models show superior performance compared to traditional works. However, these models suffer from training difficulty with non-linear activation…
This project demonstrated a methodology to estimating cooperate credibility with a Natural Language Processing approach. As cooperate transparency impacts both the credibility and possible future earnings of the firm, it is an important factor to be considered by banks and investors on risk assessments of listed firms. This approach of estimating cooperate credibility can bypass human bias and inconsistency in the risk assessment, the use of large quantitative data and neural network models provides more accurate estimation in a more efficient manner compare to manual assessment. At the beginn…
Eindhoven University of Technology（埃因霍温理工大学）；Cooperatieve Rabobank U.A.（拉博银行）
Effectively detecting anomalous nodes in attributed networks is crucial for the success of many real-world applications such as fraud and intrusion detection. Existing approaches have difficulties with three major issues: sparsity and nonlinearity capturing, residual modeling, and network smoothing. We propose Residual Graph Convolutional Network (ResGCN), an attention-based deep residual modeling approach that can tackle these issues: modeling the attributed networks with GCN allows to capture the sparsity and nonlinearity; utilizing a deep neural network allows to directly learn residual fro…
Frankfurt Institute for Advanced Studies (FIAS)（法兰克福高等研究院）；Goethe University Frankfurt（法兰克福大学）；Center for Personalized Translational Epilepsy Research (CePTER)（个性化转化癫痫研究中心）
Epilepsy is the fourth most common neurological disorder, affecting about 1% of the population at all ages. As many as 60% of people with epilepsy experience focal seizures which originate in a certain brain area and are limited to part of one cerebral hemisphere. In focal epilepsy patients, a precise surgical removal of the seizure onset zone can lead to effective seizure control or even a seizure-free outcome. Thus, correct identification of the seizure onset zone is essential. For clinical evaluation purposes, electroencephalography (EEG) recordings are commonly used. However, their interpr…
Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院保罗·C·劳特伯生物医学成像研究中心）；Research Center for Medical AI, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院医学人工智能研究中心）；Shenzhen College of Advanced Technology, University of Chinese Academy of Sciences（中国科学院大学深圳先进技术学院）；The State University of New York, Buffalo（纽约州立大学布法罗分校）
This paper proposes a multi-channel image reconstruction method, named DeepcomplexMRI, to accelerate parallel MR imaging with residual complex convolutional neural network. Different from most existing works which rely on the utilization of the coil sensitivities or prior information of predefined transforms, DeepcomplexMRI takes advantage of the availability of a large number of existing multi-channel groudtruth images and uses them as labeled data to train the deep residual convolutional neural network offline. In particular, a complex convolutional network is proposed to take into account t…
Institute for Integrated and Intelligent Systems, Griffith University, Australia（格里菲斯大学综合智能系统研究所）；School of Artificial Intelligence, Xidian University, China（西安电子科技大学人工智能学院）
Convolutional neural networks (CNNs) with residual links (ResNets) and causal dilated convolutional units have been the network of choice for deep learning approaches to speech enhancement. While residual links improve gradient flow during training, feature diminution of shallow layer outputs can occur due to repetitive summations with deeper layer outputs. One strategy to improve feature re-usage is to fuse both ResNets and densely connected CNNs (DenseNets). DenseNets, however, over-allocate parameters for feature re-usage. Motivated by this, we propose the residual-dense lattice network (RD…
Google Brain（谷歌大脑）；Stanford University（斯坦福大学）；Google（谷歌）
An emerging design principle in deep learning is that each layer of a deep artificial neural network should be able to easily express the identity transformation. This idea not only motivated various normalization techniques, such as \emph{batch normalization}, but was also key to the immense success of \emph{residual networks}. In this work, we put the principle of \emph{identity parameterization} on a more solid theoretical footing alongside further empirical progress. We first give a strikingly simple proof that arbitrarily deep linear residual networks have no spurious local optima. The sa…
