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The Residual Network (ResNet), proposed in He et al. (2015), utilized shortcut connections to significantly reduce the difficulty of training, which resulted in great performance boosts in terms of both training and generalization error. It…
Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…
Convolutional Neural Networks (CNNs) has revolutionized computer vision, but training very deep networks has been challenging due to the vanishing gradient problem. This paper explores Residual Networks (ResNet), introduced by He et al.…
In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as…
The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…
In this paper, we prove that depth with nonlinearity creates no bad local minima in a type of arbitrarily deep ResNets with arbitrary nonlinear activation functions, in the sense that the values of all local minima are no worse than the…
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,…
Augmenting neural networks with skip connections, as introduced in the so-called ResNet architecture, surprised the community by enabling the training of networks of more than 1,000 layers with significant performance gains. This paper…
Deep residual networks (ResNets) and their variants are widely used in many computer vision applications and natural language processing tasks. However, the theoretical principles for designing and training ResNets are still not fully…
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…
We analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…
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…
Deep neural networks are known to be difficult to train due to the instability of back-propagation. A deep \emph{residual network} (ResNet) with identity loops remedies this by stabilizing gradient computations. We prove a boosting theory…
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link…
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…
Deep residual learning (ResNet) is a new method for training very deep neural networks using identity map-ping for shortcut connections. ResNet has won the ImageNet ILSVRC 2015 classification task, and achieved state-of-the-art performances…
In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short…
We empirically evaluate common assumptions about neural networks that are widely held by practitioners and theorists alike. In this work, we: (1) prove the widespread existence of suboptimal local minima in the loss landscape of neural…
We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residue network (ResNet) as an effective neural network structure.…
The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…