Residual networks (ResNets) have recently achieved state-of-the-art on challenging computer vision tasks. We introduce Resnet in Resnet (RiR): a deep dual-stream architecture that generalizes ResNets and standard CNNs and is easily implemented with no computational overhead. RiR consistently improves performance over ResNets, outperforms architectures with similar amounts of augmentation on CIFAR-10, and establishes a new state-of-the-art on CIFAR-100.
Residual Neural Networks (ResNets) achieve state-of-the-art performance in many computer vision problems. Compared to plain networks without residual connections (PlnNets), ResNets train faster, generalize better, and suffer less from the so-called degradation problem. We introduce simplified (but still nonlinear) versions of ResNets and PlnNets for which these discrepancies still hold, although to a lesser degree. We establish a 1-1 mapping between simplified ResNets and simplified PlnNets, and show that they are exactly equivalent to each other in expressive power for the same computational …
Residual Network (ResNet) is the state-of-the-art architecture that realizes successful training of really deep neural network. It is also known that good weight initialization of neural network avoids problem of vanishing/exploding gradients. In this paper, simplified models of ResNets are analyzed. We argue that goodness of ResNet is correlated with the fact that ResNets are relatively insensitive to choice of initial weights. We also demonstrate how batch normalization improves backpropagation of deep ResNets without tuning initial values of weights.
Spiking neural networks (SNNs) have received significant attention for their biological plausibility. SNNs theoretically have at least the same computational power as traditional artificial neural networks (ANNs). They possess potential of achieving energy-efficiency while keeping comparable performance to deep neural networks (DNNs). However, it is still a big challenge to train a very deep SNN. In this paper, we propose an efficient approach to build a spiking version of deep residual network (ResNet). ResNet is considered as a kind of the state-of-the-art convolutional neural networks (CNNs…
The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A way to circumvent this issue is to use reversible architectures. In this paper, we propose to change the forward rule of a ResNet by adding a momentum term. The resulting networks, momentum residual neural networks (Momentum ResNets), are invertible. Unlike previous invertible architectures, they can be used as a drop-in replacement for any existing ResNet block. We show that Momentum ResNets can be interpreted in the infinitesimal s…
Tel Aviv University（特拉维夫大学）；New York University（纽约大学）
A major factor in the success of deep neural networks is the use of sophisticated architectures rather than the classical multilayer perceptron (MLP). Residual networks (ResNets) stand out among these powerful modern architectures. Previous works focused on the optimization advantages of deep ResNets over deep MLPs. In this paper, we show another distinction between the two models, namely, a tendency of ResNets to promote smoother interpolations than MLPs. We analyze this phenomenon via the neural tangent kernel (NTK) approach. First, we compute the NTK for a considered ResNet model and prove …
Residual connections significantly boost the performance of deep neural networks. However, there are few theoretical results that address the influence of residuals on the hypothesis complexity and the generalization ability of deep neural networks. This paper studies the influence of residual connections on the hypothesis complexity of the neural network in terms of the covering number of its hypothesis space. We prove that the upper bound of the covering number is the same as chain-like neural networks, if the total numbers of the weight matrices and nonlinearities are fixed, no matter wheth…
Max Planck Insitute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
Residual networks (ResNets) are a deep learning architecture that substantially improved the state of the art performance in certain supervised learning tasks. Since then, they have received continuously growing attention. ResNets have a recursive structure $x_{k+1} = x_k + R_k(x_k)$ where $R_k$ is a neural network called a residual block. This structure can be seen as the Euler discretisation of an associated ordinary differential equation (ODE) which is called a neural ODE. Recently, ResNets were proposed as the space-time approximation of ODEs which are not of this neural type. To elaborate…
Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first quantify the distance between the ResNet's hidden state trajectory and the solution of its corresponding Neural ODE. Our bound is tight and, on the negative side, does not go to 0 with depth N if the residual functions are not smooth with depth. On the positive side, we show that this smoothness is preserved by gradient descent for a ResNet with linear resi…
Institut Mines Télécom Atlantique（大西洋矿电信研究所）；LaTIM U1101 INSERM, UBL（法国国家健康与医学研究院LaTIM U1101，UBL）；LabSTIC UMR CNRS 6285, UBL（法国国家科学研究中心LabSTIC UMR 6285，UBL）
This paper addresses the understanding and characterization of residual networks (ResNet), which are among the state-of-the-art deep learning architectures for a variety of supervised learning problems. We focus on the mapping component of ResNets, which map the embedding space towards a new unknown space where the prediction or classification can be stated according to linear criteria. We show that this mapping component can be regarded as the numerical implementation of continuous flows of diffeomorphisms governed by ordinary differential equations. Especially, ResNets with shared weights ar…
Recent results in the literature indicate that a residual network (ResNet) composed of a single residual block outperforms linear predictors, in the sense that all local minima in its optimization landscape are at least as good as the best linear predictor. However, these results are limited to a single residual block (i.e., shallow ResNets), instead of the deep ResNets composed of multiple residual blocks. We take a step towards extending this result to deep ResNets. We start by two motivating examples. First, we show that there exist datasets for which all local minima of a fully-connected R…
Faculty of Engineering and Information Technology（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）；Suncorp Group Limited（Suncorp集团有限公司）
We show that Residual Networks (ResNet) is equivalent to boosting feature representation, without any modification to the underlying ResNet training algorithm. A regret bound based on Online Gradient Boosting theory is proved and suggests that ResNet could achieve Online Gradient Boosting regret bounds through neural network architectural changes with the addition of a shrinkage parameter in the identity skip-connections and using residual modules with max-norm bounds. Through this relation between ResNet and Online Boosting, novel feature representation boosting algorithms can be constructed …
Weizmann Institute of Science（魏茨曼科学研究所）；Microsoft Research（微软研究院）
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just the residual of the previous layer's output and the target output. Thus, we should expect that the trained network is no worse than what we can obtain if we remove the residual layers and train a shallower network instead. However, due to the non-convexity of the optimization problem, it is not at all clear that ResNets indeed achieve this behavior, rather tha…
Peking University（北京大学）；Georgia Institute of Technology（佐治亚理工学院）
Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. This paper studies this fundamental problem in deep learning from a so-called "neural tangent kernel" perspective. Specifically, we first show that under proper conditions, as the width goes to infinity, training deep ResNets can be viewed as learning reproducing kernel functions with some kernel function. We then compare the kernel of deep ResNets with that of deep FFNets and discover that the class…
Residual Networks (ResNets) have become state-of-the-art models in deep learning and several theoretical studies have been devoted to understanding why ResNet works so well. One attractive viewpoint on ResNet is that it is optimizing the risk in a functional space by combining an ensemble of effective features. In this paper, we adopt this viewpoint to construct a new gradient boosting method, which is known to be very powerful in data analysis. To do so, we formalize the gradient boosting perspective of ResNet mathematically using the notion of functional gradients and propose a new method ca…
Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far the question of whether Neural ODEs and i-ResNets can model any continuous invertible function remained unresolved. Here, we show that both of these models are limited in their approximation capabilities. We then prove that any homeomorphism on a $p$-dimensional Euclidean space can be approximated by a Neural ODE operating on a $2p$-dimensional Euclidean space…
Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which suggest that the forward and backward signals can be directly propagated from one block to any other block, when using identity mappings as the skip connections and after-addition activation. A series of ablation experiments support the importance of these identity mappings. This motivates us to propose a new residual unit, which makes training easier and impr…
Center for Brains, Minds, and Machines（脑、心智与机器中心）；McGovern Institute for Brain Research（麦戈文脑科学研究所）；Massachusetts Institute of Technology（麻省理工学院）
We discuss relations between Residual Networks (ResNet), Recurrent Neural Networks (RNNs) and the primate visual cortex. We begin with the observation that a special type of shallow RNN is exactly equivalent to a very deep ResNet with weight sharing among the layers. A direct implementation of such a RNN, although having orders of magnitude fewer parameters, leads to a performance similar to the corresponding ResNet. We propose 1) a generalization of both RNN and ResNet architectures and 2) the conjecture that a class of moderately deep RNNs is a biologically-plausible model of the ventral str…
University of Toronto（多伦多大学）；Uber Advanced Technologies Group（Uber先进技术集团）
Deep residual networks (ResNets) have significantly pushed forward the state-of-the-art on image classification, increasing in performance as networks grow both deeper and wider. However, memory consumption becomes a bottleneck, as one needs to store the activations in order to calculate gradients using backpropagation. We present the Reversible Residual Network (RevNet), a variant of ResNets where each layer's activations can be reconstructed exactly from the next layer's. Therefore, the activations for most layers need not be stored in memory during backpropagation. We demonstrate the effect…
Sri Sathya Sai Institute of Higher Learning（斯里萨蒂亚赛高等教育学院）；Department of Mathematics and Computer Science（数学与计算机科学系）；Prasanthi Nilayam, AP, India（普拉萨蒂尼莱亚姆，安得拉邦，印度）
One of the ways to train deep neural networks effectively is to use residual connections. Residual connections can be classified as being either identity connections or bridge-connections with a reshaping convolution. Empirical observations on CIFAR-10 and CIFAR-100 datasets using a baseline Resnet model, with bridge-connections removed, have shown a significant reduction in accuracy. This reduction is due to lack of contribution, in the form of feature maps, by the bridge-connections. Hence bridge-connections are vital for Resnet. However, all feature maps in the bridge-connections are consid…
University of Bremen（不来梅大学）；Vector Institute（向量研究所）；University of Toronto（多伦多大学）
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant …
In this paper we consider utilizing a residual neural network (ResNet) to solve ordinary differential equations. Stochastic gradient descent method is applied to obtain the optimal parameter set of weights and biases of the network. We apply forward Euler, Runge-Kutta2 and Runge-Kutta4 finite difference methods to generate three sets of targets training the ResNet and carry out the target study. The well trained ResNet behaves just as its counterpart of the corresponding one-step finite difference method. In particular, we carry out (1) the architecture study in terms of number of hidden layer…
We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 data set. We linearize these networks at the level of residual units and network stages, and the singular value decomposition is used in the stability analysis of these components. It is found that most of the singular values of the linearizations of residual units are 1 and, in spi…
Researchers often treat data-driven and theory-driven models as two disparate or even conflicting methods in travel behavior analysis. However, the two methods are highly complementary because data-driven methods are more predictive but less interpretable and robust, while theory-driven methods are more interpretable and robust but less predictive. Using their complementary nature, this study designs a theory-based residual neural network (TB-ResNet) framework, which synergizes discrete choice models (DCMs) and deep neural networks (DNNs) based on their shared utility interpretation. The TB-Re…
Cogent Labs（Cogent实验室）；University of Torino（都灵大学）；Collegio Carlo Alberto（阿尔贝托国王学院）
Modern neural networks (NN) featuring a large number of layers (depth) and units per layer (width) have achieved a remarkable performance across many domains. While there exists a vast literature on the interplay between infinitely wide NNs and Gaussian processes, a little is known about analogous interplays with respect to infinitely deep NNs. NNs with independent and identically distributed (i.i.d.) initializations exhibit undesirable forward and backward propagation properties as the number of layers increases. To overcome these drawbacks, Peluchetti and Favaro (2020) considered fully-conne…
We derive finite width and depth corrections for the Neural Tangent Kernel (NTK) of ResNets and DenseNets. Our analysis reveals that finite size residual architectures are initialized much closer to the "kernel regime" than their vanilla counterparts: while in networks that do not use skip connections, convergence to the NTK requires one to fix the depth, while increasing the layers' width. Our findings show that in ResNets, convergence to the NTK may occur when depth and width simultaneously tend to infinity, provided with a proper initialization. In DenseNets, however, convergence of the NTK…
University of New South Wales（新南威尔士大学）；Australian Center for Cyber, University of New South Wales（新南威尔士大学澳大利亚网络中心）；Sangfor Technologies Inc.（深信服科技股份有限公司）
High false alarm rate and low detection rate are the major sticking points for unknown threat perception. To address the problems, in the paper, we present a densely connected residual network (Densely-ResNet) for attack recognition. Densely-ResNet is built with several basic residual units, where each of them consists of a series of Conv-GRU subnets by wide connections. Our evaluation shows that Densely-ResNet can accurately discover various unknown threats that appear in edge, fog and cloud layers and simultaneously maintain a much lower false alarm rate than existing algorithms.
In recent years residual neural networks (ResNets) as introduced by [He, K., Zhang, X., Ren, S., and Sun, J., Proceedings of the IEEE conference on computer vision and pattern recognition (2016), 770-778] have become very popular in a large number of applications, including in image classification and segmentation. They provide a new perspective in training very deep neural networks without suffering the vanishing gradient problem. In this article we show that ResNets are able to approximate solutions of Kolmogorov partial differential equations (PDEs) with constant diffusion and possibly nonl…
Tsinghua University（清华大学）；City University of Hong Kong（香港城市大学）
In this paper, we aim to understand Residual Network (ResNet) in a scientifically sound way by providing a bridge between ResNet and Feynman path integral. In particular, we prove that the effect of residual block is equivalent to partial differential equation, and the ResNet transforming process can be equivalently converted to Feynman path integral. These conclusions greatly help us mathematically understand the advantage of ResNet in addressing the gradient vanishing issue. More importantly, our analyses offer a path integral view of ResNet, and demonstrate that the output of certain networ…
Various powerful deep neural network architectures have made great contribution to the exciting successes of deep learning in the past two decades. Among them, deep Residual Networks (ResNets) are of particular importance because they demonstrated great usefulness in computer vision by winning the first place in many deep learning competitions. Also, ResNets were the first class of neural networks in the development history of deep learning that are really deep. It is of mathematical interest and practical meaning to understand the convergence of deep ResNets. We aim at characterizing the conv…
Peking University（北京大学）；Shandong University（山东大学）；Samsung Research China – Beijing (SRC-B)（三星中国研究院——北京（SRC-B））
The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we also have an adaptive time stepping for ResNets to ensure both stability and performance? In this study, we analyze the effects of time stepping on the Euler method and ResNets. We establish a stability condition for ResNets with step sizes and weight parameters, and point out th…
Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear. In this paper, we present a novel ODE model by adding a damping term. It can be shown that the proposed model can recover both a ResNet and a CNN by adjusting an interpolation coefficient. Therefore, the damped ODE model provides a unified framework for the interpretation of residual and non-residual networks. The Lyapunov analysis reveals better stability of the proposed model, and thus yields robust…
Georgia Tech（佐治亚理工学院）；Duke University（杜克大学）；Institute of Advanced Study（高等研究院）；Peking University（北京大学）；CMU（卡内基梅隆大学）
Residual Network (ResNet) is undoubtedly a milestone in deep learning. ResNet is equipped with shortcut connections between layers, and exhibits efficient training using simple first order algorithms. Despite of the great empirical success, the reason behind is far from being well understood. In this paper, we study a two-layer non-overlapping convolutional ResNet. Training such a network requires solving a non-convex optimization problem with a spurious local optimum. We show, however, that gradient descent combined with proper normalization, avoids being trapped by the spurious local optimum…
IBM Research（IBM研究）；Fusemachines Inc.（Fusemachines公司）；UMD（马里兰大学（UMD））；UT Austin（德克萨斯大学奥斯汀分校（UT Austin））
Very deep convolutional neural networks offer excellent recognition results, yet their computational expense limits their impact for many real-world applications. We introduce BlockDrop, an approach that learns to dynamically choose which layers of a deep network to execute during inference so as to best reduce total computation without degrading prediction accuracy. Exploiting the robustness of Residual Networks (ResNets) to layer dropping, our framework selects on-the-fly which residual blocks to evaluate for a given novel image. In particular, given a pretrained ResNet, we train a policy ne…
Tsinghua University（清华大学）；Technische Universität Graz（格拉茨工业大学）；Xi’an Jiaotong University（西安交通大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Despite the rapid progress of neuromorphic computing, inadequate capacity and insufficient representation power of spiking neural networks (SNNs) severely restrict their application scope in practice. Residual learning and shortcuts have been evidenced as an important approach for training deep neural networks, but rarely did previous work assess their applicability to the characteristics of spike-based communication and spatiotemporal dynamics. In this paper, we first identify that this negligence leads to impeded information flow and the accompanying degradation problem in previous residual …
Shanghai Jiao Tong University（上海交通大学）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；the Hong Kong University of Science and Technology（香港科技大学）
Semantic road region segmentation is a high-level task, which paves the way towards road scene understanding. This paper presents a residual network trained for semantic road segmentation. Firstly, we represent the projections of road disparities in the v-disparity map as a linear model, which can be estimated by optimizing the v-disparity map using dynamic programming. This linear model is then utilized to reduce the redundant information in the left and right road images. The right image is also transformed into the left perspective view, which greatly enhances the road surface similarity be…
We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system's viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is…
We demonstrate that in residual neural networks (ResNets) dynamical isometry is achievable irrespectively of the activation function used. We do that by deriving, with the help of Free Probability and Random Matrix Theories, a universal formula for the spectral density of the input-output Jacobian at initialization, in the large network width and depth limit. The resulting singular value spectrum depends on a single parameter, which we calculate for a variety of popular activation functions, by analyzing the signal propagation in the artificial neural network. We corroborate our results with n…
University of Applied Sciences Aschaffenburg（阿沙芬堡应用科学大学）；University of Kassel（卡塞尔大学）
In this article, we present a novel approach to detect starting motions of cyclists in real world traffic scenarios based on Motion History Images (MHIs). The method uses a deep Convolutional Neural Network (CNN) with a residual network architecture (ResNet), which is commonly used in image classification and detection tasks. By combining MHIs with a ResNet classifier and performing a frame by frame classification of the MHIs, we are able to detect starting motions in image sequences. The detection is performed using a wide angle stereo camera system at an urban intersection. We compare our al…
There is an analogy between the ResNet (Residual Network) architecture for deep neural networks and an Euler solver for an ODE. The transformation performed by each layer resembles an Euler step in solving an ODE. We consider the Heun Method, which involves a single predictor-corrector cycle, and complete the analogy, building a predictor-corrector variant of ResNet, which we call a HeunNet. Just as Heun's method is more accurate than Euler's, experiments show that HeunNet achieves high accuracy with low computational (both training and test) time compared to both vanilla recurrent neural netw…
Tsinghua University（清华大学）；Shanghai Jiao Tong University（上海交通大学）；PCL Research Center of Networks and Communications, Peng Cheng Laboratory（鹏城实验室网络通信PCL研究中心）；The University of Melbourne（墨尔本大学）
Skip connections are an essential component of current state-of-the-art deep neural networks (DNNs) such as ResNet, WideResNet, DenseNet, and ResNeXt. Despite their huge success in building deeper and more powerful DNNs, we identify a surprising security weakness of skip connections in this paper. Use of skip connections allows easier generation of highly transferable adversarial examples. Specifically, in ResNet-like (with skip connections) neural networks, gradients can backpropagate through either skip connections or residual modules. We find that using more gradients from the skip connecti…
Microsoft Research（微软研究院）；Southwest Jiaotong University（西南交通大学）；Xidian University（西安电子科技大学）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Forecasting the flow of crowds is of great importance to traffic management and public safety, yet a very challenging task affected by many complex factors, such as inter-region traffic, events and weather. In this paper, we propose a deep-learning-based approach, called ST-ResNet, to collectively forecast the in-flow and out-flow of crowds in each and every region through a city. We design an end-to-end structure of ST-ResNet based on unique properties of spatio-temporal data. More specifically, we employ the framework of the residual neural networks to model the temporal closeness, period, a…
Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, these models have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual r…
Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this problem, we propose Network Implosion, it erases multiple layers from Residual Networks without degrading accuracy. Our key idea is to introduce a priority term that identifies the importance of a layer; we can select unimportant layers according to the priority and erase them after…
Universal Approximation Constraints of Narrow ResNets: The Tunnel Effect
Technical University of Munich（慕尼黑工业大学）；Munich Data Science Institute (MDSI)（慕尼黑数据科学研究所）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；TU Wien（维也纳工业大学）
Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural networks, this work presents a mean-field analysis of deep residual networks, based on a line of works that interpret the continuum limit of the deep residual network as an ordinary differential equation when the network capacity tends to infinity. Specifically, we propose a new continuum limit of deep residual networks, which enjoys a good lan…
For the past 5 years, the ILSVRC competition and the ImageNet dataset have attracted a lot of interest from the Computer Vision community, allowing for state-of-the-art accuracy to grow tremendously. This should be credited to the use of deep artificial neural network designs. As these became more complex, the storage, bandwidth, and compute requirements increased. This means that with a non-distributed approach, even when using the most high-density server available, the training process may take weeks, making it prohibitive. Furthermore, as datasets grow, the representation learning potentia…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Google（谷歌）
We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations at input and output layers, which are fixed throughout training, both GD and SGD with zero initialization on all hidden weights can converge to the global minimum of the training loss. Moreover, when specializing to appropriate Gaussian random linear transformations, GD and SGD provably optimize wide enough deep linear ResNets. Compared with the global conve…
Various deep neural network architectures (DNNs) maintain massive vital records in computer vision. While drawing attention worldwide, the design of the overall structure lacks general guidance. Based on the relationship between DNN design and numerical differential equations, we performed a fair comparison of the residual design with higher-order perspectives. We show that the widely used DNN design strategy, constantly stacking a small design (usually 2-3 layers), could be easily improved, supported by solid theoretical knowledge and with no extra parameters needed. We reorganise the residua…
Field theory for optimal signal propagation in ResNets
Institute for Advanced Simulation (IAS-6), Jülich Research Centre（先进模拟研究所（IAS-6）、尤利希研究中心）；RWTH Aachen University（亚琛工业大学）；Department of Physics, Faculty 1, RWTH Aachen University（物理系，亚琛工业大学）
Tencent Youtu Lab（腾讯优图实验室）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
Although residual connection enables training very deep neural networks, it is not friendly for online inference due to its multi-branch topology. This encourages many researchers to work on designing DNNs without residual connections at inference. For example, RepVGG re-parameterizes multi-branch topology to a VGG-like (single-branch) model when deploying, showing great performance when the network is relatively shallow. However, RepVGG can not transform ResNet to VGG equivalently because re-parameterizing methods can only be applied to linear blocks and the non-linear layers (ReLU) have to b…
Salesforce Research（赛富时研究院）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Montréal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Residual networks (ResNet) and weight normalization play an important role in various deep learning applications. However, parameter initialization strategies have not been studied previously for weight normalized networks and, in practice, initialization methods designed for un-normalized networks are used as a proxy. Similarly, initialization for ResNets have also been studied for un-normalized networks and often under simplified settings ignoring the shortcut connection. To address these issues, we propose a novel parameter initialization strategy that avoids explosion/vanishment of informa…
