Convolutional neural networks typically contain several downsampling operators, such as strided convolutions or pooling layers, that progressively reduce the resolution of intermediate representations. This provides some shift-invariance while reducing the computational complexity of the whole architecture. A critical hyperparameter of such layers is their stride: the integer factor of downsampling. As strides are not differentiable, finding the best configuration either requires cross-validation or discrete optimization (e.g. architecture search), which rapidly become prohibitive as the search space grows exponentially with the number of downsampling layers. Hence, exploring this search space by gradient descent would allow finding better configurations at a lower computational cost. This work introduces DiffStride, the first downsampling layer with learnable strides. Our layer learns the size of a cropping mask in the Fourier domain, that effectively performs resizing in a differentiable way. Experiments on audio and image classification show the generality and effectiveness of our solution: we use DiffStride as a drop-in replacement to standard downsampling layers and outperform them. In particular, we show that introducing our layer into a ResNet-18 architecture allows keeping consistent high performance on CIFAR10, CIFAR100 and ImageNet even when training starts from poor random stride configurations. Moreover, formulating strides as learnable variables allows us to introduce a regularization term that controls the computational complexity of the architecture. We show how this regularization allows trading off accuracy for efficiency on ImageNet.
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a reproducing kernel Hilbert space, the CNN parameters can be represented as a low-rank matrix, which can be relaxed to obtain a convex optimization problem. For learning two-layer convolutional neural networks, we prove that the generalization error obtained by a convexified CNN converges to that of the best possible CNN. For learning deeper networks, we train CCNNs…
University of Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡大学）；Waldkrankenhaus St. Marien（圣玛丽森林医院）；University Hospital Erlangen（埃尔朗根大学医院）
Measurement of stride-related, biomechanical parameters is the common rationale for objective gait impairment scoring. State-of-the-art double integration approaches to extract these parameters from inertial sensor data are, however, limited in their clinical applicability due to the underlying assumptions. To overcome this, we present a method to translate the abstract information provided by wearable sensors to context-related expert features based on deep convolutional neural networks. Regarding mobile gait analysis, this enables integration-free and data-driven extraction of a set of 8 spa…
University of Texas at Austin（得克萨斯大学奥斯汀分校）；UCLA（加州大学洛杉矶分校）
We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including one-dimensional and two-dimensional "patch and stride" convolutions. Our algorithm-- $Convotron$ -- is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochast…
University of Maryland, College Park（马里兰大学帕克分校）；NVIDIA Corporation（英伟达公司）
Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the orthogonality of convolutional layers is not systematically studied: some of these designs are not exactly orthogonal, while others only consider standard convolutional layers and propose specific classes of their realizations. To address this problem, we propose a theoretical framework for orthogonal convolutional layers, which establishes the equivalence betwee…
LTS2；EPFL（洛桑联邦理工学院）；IDCOM；University of Edinburgh（爱丁堡大学）
Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.
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…
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…
China University of Geosciences（中国地质大学）；University of Kentucky（肯塔基大学）
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresponding to a convolutional kernel bounded around $1$. We propose a penalty function that can be used in the optimization of a convolutional neural network to constrain the singular values of the transformation matrix around $1$. We derive an algorithm to carry out the gradient des…
Modern convolutional networks are not shift-invariant, as small input shifts or translations can cause drastic changes in the output. Commonly used downsampling methods, such as max-pooling, strided-convolution, and average-pooling, ignore the sampling theorem. The well-known signal processing fix is anti-aliasing by low-pass filtering before downsampling. However, simply inserting this module into deep networks degrades performance; as a result, it is seldomly used today. We show that when integrated correctly, it is compatible with existing architectural components, such as max-pooling and s…
Function Space and Critical Points of Linear Convolutional Networks
KTH Royal Institute of Technology（瑞典皇家理工学院）；UCLA（加州大学洛杉矶分校）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；Amazon AWS AI Labs（亚马逊AWS人工智能实验室）
In this paper, we propose a fixed convolutional layer with an order of smoothness not only for avoiding checkerboard artifacts in convolutional neural networks (CNNs) but also for enhancing the performance of CNNs, where the smoothness of its filter kernel can be controlled by a parameter. It is well-known that a number of CNNs generate checkerboard artifacts in both of two process: forward-propagation of upsampling layers and backward-propagation of strided convolutional layers. The proposed layer can perfectly prevent checkerboard artifacts caused by strided convolutional layers or upsamplin…
We propose an extension of Convolutional Neural Networks (CNNs) to graph-structured data, including strided convolutions and data augmentation on graphs. Our method matches the accuracy of state-of-the-art CNNs when applied on images, without any prior about their 2D regular structure. On fMRI data, we obtain a significant gain in accuracy compared with existing graph-based alternatives.
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.
Missouri University of Science and Technology（密苏里科技大学）
Convolutional neural networks (CNNs) have made resounding success in many computer vision tasks such as image classification and object detection. However, their performance degrades rapidly on tougher tasks where images are of low resolution or objects are small. In this paper, we point out that this roots in a defective yet common design in existing CNN architectures, namely the use of strided convolution and/or pooling layers, which results in a loss of fine-grained information and learning of less effective feature representations. To this end, we propose a new CNN building block called SP…
USEFUSE: Uniform Stride for Enhanced Performance in Fused Layer Architecture of Deep Neural Networks
Department of Mechanical Systems Engineering（机械系统工程系）；Kumoh National Institute of Technology（Kumoh国立技术学院）；Faculty of Informatics and Data Science（信息与数据科学学院）；University of Regensburg（雷根斯堡大学）；Department of Computer Engineering（计算机工程系）；Chosun University（全州大学）
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular network connections that not only demand extra representation efforts but also do not fit well on parallel computation. We introduce structured sparsity at various scales for convolutional neural networks, which are channel wise, kernel wise and intra kernel strided sparsity. This structured sparsity is very advantageous for direct computational resource sa…
Xsensor Technology Corp（Xsensor科技公司）；University of Alberta（阿尔伯塔大学）
Multivariate time series classification is a high value and well-known problem in machine learning community. Feature extraction is a main step in classification tasks. Traditional approaches employ hand-crafted features for classification while convolutional neural networks (CNN) are able to extract features automatically. In this paper, we use dilated convolutional neural network for multivariate time series classification. To deploy dilated CNN, a multivariate time series is transformed into an image-like style and stacks of dilated and strided convolutions are applied to extract in and bet…
Predicting the evolution of a representative sample of a material with microstructure is a fundamental problem in homogenization. In this work we propose a graph convolutional neural network that utilizes the discretized representation of the initial microstructure directly, without segmentation or clustering. Compared to feature-based and pixel-based convolutional neural network models, the proposed method has a number of advantages: (a) it is deep in that it does not require featurization but can benefit from it, (b) it has a simple implementation with standard convolutional filters and laye…
The driving force behind convolutional networks - the most successful deep learning architecture to date, is their expressive power. Despite its wide acceptance and vast empirical evidence, formal analyses supporting this belief are scarce. The primary notions for formally reasoning about expressiveness are efficiency and inductive bias. Expressive efficiency refers to the ability of a network architecture to realize functions that require an alternative architecture to be much larger. Inductive bias refers to the prioritization of some functions over others given prior knowledge regarding a t…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Basel（巴塞尔大学）
Thanks to the use of convolution and pooling layers, convolutional neural networks were for a long time thought to be shift-invariant. However, recent works have shown that the output of a CNN can change significantly with small shifts in input: a problem caused by the presence of downsampling (stride) layers. The existing solutions rely either on data augmentation or on anti-aliasing, both of which have limitations and neither of which enables perfect shift invariance. Additionally, the gains obtained from these methods do not extend to image patterns not seen during training. To address thes…
The Riemannian Geometry Associated to Gradient Flows of Linear Convolutional Networks
UM6P College of Computing（穆罕默德六世理工大学计算机学院）；KTH Royal Inst. of Technology & Digital Futures（皇家理工学院 & Digital Futures）；LMU Dept. of Math & MCML（慕尼黑大学数学系 & MCML）
Convolutional neural networks (CNNs) are a representative class of deep learning algorithms including convolutional computation that perform translation-invariant classification of input data based on their hierarchical architecture. However, classical convolutional neural network learning methods use the steepest descent algorithm for training, and the learning performance is greatly influenced by the initial weight settings of the convolutional and fully connected layers, requiring re-tuning to achieve better performance under different model structures and data. Combining the strengths of t…
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features, including a bias towards learning oversmoothed and homophilic functions, which are not easily diagnosed due to the complex nature of these algorithms. We propose to bridge this gap in understanding by studying the neural tangent kernel of sheaf convolutional networks--a topological generalization of graph convolutional networks. To this end, we derive a par…
Imperial College London（帝国理工学院）；Hellebore Capital Limited（Hellebore Capital有限公司）；Ecole Polytechnique（巴黎综合理工学院）
We propose Significance-Offset Convolutional Neural Network, a deep convolutional network architecture for regression of multivariate asynchronous time series. The model is inspired by standard autoregressive (AR) models and gating mechanisms used in recurrent neural networks. It involves an AR-like weighting system, where the final predictor is obtained as a weighted sum of adjusted regressors, while the weights are datadependent functions learnt through a convolutional network. The architecture was designed for applications on asynchronous time series and is evaluated on such datasets: a hed…
Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -- and building on other rec…
Institute of Biomedical Sciences, Academia Sinica（中央研究院生物医学科学研究所）
The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the identification of such patterns may be important for certain applications and suggest providing neural networks with information that fully describes the combinatorial patterns of input entries and allows the network to determine what is relevant for prediction. To demonstrate the feasibility of this approach, we present a combinatorial convolutional neural net…
KTH Royal Institute of Technology（瑞典皇家理工学院）；MessageBird（MessageBird公司）；University of Washington（华盛顿大学）
Sum-Product Networks (SPNs) are hierarchical, graphical models that combine benefits of deep learning and probabilistic modeling. SPNs offer unique advantages to applications demanding exact probabilistic inference over high-dimensional, noisy inputs. Yet, compared to convolutional neural nets, they struggle with capturing complex spatial relationships in image data. To alleviate this issue, we introduce Deep Generalized Convolutional Sum-Product Networks (DGC-SPNs), which encode spatial features in a way similar to CNNs, while preserving the validity of the probabilistic SPN model. As opposed…
I present a new way to parallelize the training of convolutional neural networks across multiple GPUs. The method scales significantly better than all alternatives when applied to modern convolutional neural networks.
We propose a new way of incorporating temporal information present in videos into Spatial Convolutional Neural Networks (ConvNets) trained on images, that avoids training Spatio-Temporal ConvNets from scratch. We describe several initializations of weights in 3D Convolutional Layers of Spatio-Temporal ConvNet using 2D Convolutional Weights learned from ImageNet. We show that it is important to initialize 3D Convolutional Weights judiciously in order to learn temporal representations of videos. We evaluate our methods on the UCF-101 dataset and demonstrate improvement over Spatial ConvNets.
We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and appropriately chosen convolutional kernels, already two-parameter families of convolutional neural networks have an infinite VC dimension, despite being invariant to the action of an infinite group.
Ensemble learning is a method of combining multiple trained models to improve model accuracy. We propose the usage of such methods, specifically ensemble average, inside Convolutional Neural Network (CNN) architectures by replacing the single convolutional layers with Inner Average Ensembles (IEA) of multiple convolutional layers. Empirical results on different benchmarking datasets show that CNN models using IEA outperform those with regular convolutional layers. A visual and a similarity score analysis of the features generated from IEA explains why it boosts the model performance.
Deep convolutional neural networks take GPU days of compute time to train on large data sets. Pedestrian detection for self driving cars requires very low latency. Image recognition for mobile phones is constrained by limited processing resources. The success of convolutional neural networks in these situations is limited by how fast we can compute them. Conventional FFT based convolution is fast for large filters, but state of the art convolutional neural networks use small, 3x3 filters. We introduce a new class of fast algorithms for convolutional neural networks using Winograd's minimal fil…
Technische Universität Darmstadt（达姆施塔特工业大学）；Concordia University（康考迪亚大学）
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of the aposteriori probability a rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification it is possible to circumvent the curse of dimensionality by convolutional neural networks.
Dipartimento di Matematica, Università di Bologna（博洛尼亚大学数学系）
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the network. While for fully-connected networks the properties of convergence to Gaussian processes have been studied extensively, little is known about situations in which the output from a convolutional network approaches a multivariate normal distribution.
While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can be better represented as a general graph instead of a regular grid. Although recent algorithms that adapt CNNs to graphs have shown promising results, they mostly neglect learning explicit operations for edge features while focusing on vertex features alone. We propose new formulations for convolutional, pooling, and fully connected layers for neural networ…
Leibniz University of Hannover（莱布尼茨汉诺威大学）；University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Finding a well-performing architecture is often tedious for both DL practitioners and researchers, leading to tremendous interest in the automation of this task by means of neural architecture search (NAS). Although the community has made major strides in developing better NAS methods, the quality of scientific empirical evaluations in the young field of NAS is still lacking behind that of other areas of machine learning. To address this issue, we describe a set of possible issues and ways to avoid them, leading to the NAS best practices checklist available at http://automl.org/nas_checklist.p…
Uppsala University（乌普萨拉大学）；Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）
The convolutional neural network (CNN) remains an essential tool in solving computer vision problems. Standard convolutional architectures consist of stacked layers of operations that progressively downscale the image. Aliasing is a well-known side-effect of downsampling that may take place: it causes high-frequency components of the original signal to become indistinguishable from its low-frequency components. While downsampling takes place in the max-pooling layers or in the strided-convolutions in these models, there is no explicit mechanism that prevents aliasing from taking place in these…
In this paper, we introduce Channel-wise recurrent convolutional neural networks (RecNets), a family of novel, compact neural network architectures for computer vision tasks inspired by recurrent neural networks (RNNs). RecNets build upon Channel-wise recurrent convolutional (CRC) layers, a novel type of convolutional layer that splits the input channels into disjoint segments and processes them in a recurrent fashion. In this way, we simulate wide, yet compact models, since the number of parameters is vastly reduced via the parameter sharing of the RNN formulation. Experimental results on the…
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.
Cornell University（康奈尔大学）；Augsburg University（奥格斯堡大学）；Technische Universität München（慕尼黑工业大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）
Deep convolutional neural networks are generally regarded as robust function approximators. So far, this intuition is based on perturbations to external stimuli such as the images to be classified. Here we explore the robustness of convolutional neural networks to perturbations to the internal weights and architecture of the network itself. We show that convolutional networks are surprisingly robust to a number of internal perturbations in the higher convolutional layers but the bottom convolutional layers are much more fragile. For instance, Alexnet shows less than a 30% decrease in classific…
Convolutional neural networks are very popular nowadays. Training neural networks is not an easy task. Each convolution corresponds to a structured transformation matrix. In order to help avoid the exploding/vanishing gradient problem, it is desirable that the singular values of each transformation matrix are not large/small in the training process. We propose three new regularization terms for a convolutional kernel tensor to constrain the singular values of each transformation matrix. We show how to carry out the gradient type methods, which provides new insight about the training of convolu…
The goal of this study was to improve the post-processing of precipitation forecasts using convolutional neural networks (CNNs). Instead of post-processing forecasts on a per-pixel basis, as is usually done when employing machine learning in meteorological post-processing, input forecast images were combined and transformed into probabilistic output forecast images using fully convolutional neural networks. CNNs did not outperform regularized logistic regression. Additionally, an ablation analysis was performed. Combining input forecasts from a global low-resolution weather model and a regiona…
University of Oxford（牛津大学）；Katholische Universität Eichstätt–Ingolstadt（艾希施泰特-英戈尔施塔特天主教大学）
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In this paper, we establish a connection between both network architectures. Using this connection, we show that all upper and lower bounds concerning approximation rates of {fully-connected} neural networks for functions $f \in \mathcal{C}$ -- for an arbitrary function class $\mathcal{C}$ -- translate to essentially the same bounds concerning approximation rates of convolutional neural networks for functions $f \in {\ma…
Latest results indicate that features learned via convolutional neural networks outperform previous descriptors on classification tasks by a large margin. It has been shown that these networks still work well when they are applied to datasets or recognition tasks different from those they were trained on. However, descriptors like SIFT are not only used in recognition but also for many correspondence problems that rely on descriptor matching. In this paper we compare features from various layers of convolutional neural nets to standard SIFT descriptors. We consider a network that was trained o…
Science and Technology on Electronic Information Control Laboratory（电子信息控制科技实验室）
A novel and efficient end-to-end learning model for automatic modulation classification is proposed for wireless spectrum monitoring applications, which automatically learns from the time domain in-phase and quadrature data without requiring the design of hand-crafted expert features. With the intuition of convolutional layers with pooling serving as the role of front-end feature distillation and dimensionality reduction, sequential convolutional recurrent neural networks are developed to take complementary advantage of parallel computing capability of convolutional neural networks and tempora…
The freedom of fast iterations of distributed deep learning tasks is crucial for smaller companies to gain competitive advantages and market shares from big tech giants. HorovodRunner brings this process to relatively accessible spark clusters. There have been, however, no benchmark tests on HorovodRunner per se, nor specifically graph convolutional network (GCN, hereafter), and very limited scalability benchmark tests on Horovod, the predecessor requiring custom built GPU clusters. For the first time, we show that Databricks' HorovodRunner achieves significant lift in scaling efficiency for t…
The University of Tokyo（东京大学）；Singapore University of Technology and Design（新加坡科技设计大学）
Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored. In this paper, we present a convolutional neural network for semantic segmentation and object recognition with 3D point clouds. At the core of our network is pointwise convolution, a new convolution operator that can be applied at each point of a point cloud. Our fully convolutional network design, while being surprisingly simple to implement, can yield com…
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the global minimum under a planted model assumption, given sufficiently many training samples from a Gaussian distribution. We also identify a phase transition phenomenon in recovering the global minimum for the relaxation.
We study channel number reduction in combination with weight binarization (1-bit weight precision) to trim a convolutional neural network for a keyword spotting (classification) task. We adopt a group-wise splitting method based on the group Lasso penalty to achieve over 50% channel sparsity while maintaining the network performance within 0.25% accuracy loss. We show an effective three-stage procedure to balance accuracy and sparsity in network training.
In view of the large amount of calculation and long calculation time of convolutional neural network (CNN), this paper proposes a convolutional neural network hardware accelerator based on field programmable logic gate array (FPGA). First, through in-depth analysis of the forward operation principle of the convolutional layer and exploration of the parallelism of the convolutional layer operation, a hardware architecture of input channel parallelism, output channel parallelism and convolution window deep pipeline is designed. Then in the above architecture, a fully parallel multiplication-addi…
East China University of Science and Technology（华东理工大学）
With the improvement of computer performance and the increase of data volume, the object detection based on convolutional neural network (CNN) has become the main algorithm for object detection. This paper summarizes the research progress of convolutional neural networks and their applications in object detection, and focuses on analyzing and discussing a specific idea and method of applying convolutional neural networks for object detection, pointing out the current deficiencies and future development direction.
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…
