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Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural…

Analysis of PDEs · Mathematics 2022-05-11 M. Herty , A. Thuenen , T. Trimborn , G. Visconti

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.…

Machine Learning · Computer Science 2021-06-02 Zhen Chen , Dongbin Xiu

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…

Machine Learning · Computer Science 2021-06-11 Alain-Sam Cohen , Rama Cont , Alain Rossier , Renyuan Xu

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,…

Machine Learning · Computer Science 2020-04-15 Lisa Gaedke-Merzhäuser , Alena Kopaničáková , Rolf Krause

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…

Machine Learning · Computer Science 2021-02-23 Viktor Reshniak , Clayton Webster

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…

Neural and Evolutionary Computing · Computer Science 2017-05-23 Sihan Li , Jiantao Jiao , Yanjun Han , Tsachy Weissman

Residual connections remain ubiquitous in modern neural network architectures nearly a decade after their introduction. Their widespread adoption is often credited to their dramatically improved trainability: residual networks train faster,…

Machine Learning · Computer Science 2025-06-18 Christian H. X. Ali Mehmeti-Göpel , Michael Wand

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…

Machine Learning · Computer Science 2018-06-15 Furong Huang , Jordan Ash , John Langford , Robert Schapire

The Wide Residual Networks (Wide-ResNets), a shallow but wide model variant of the Residual Networks (ResNets) by stacking a small number of residual blocks with large channel sizes, have demonstrated outstanding performance on multiple…

Computer Vision and Pattern Recognition · Computer Science 2021-02-09 Liang-Chieh Chen , Huiyu Wang , Siyuan Qiao

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…

Machine Learning · Computer Science 2026-02-25 Jinshu Huang , Mingfei Sun , Chunlin Wu

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…

Computer Vision and Pattern Recognition · Computer Science 2021-05-12 Fereshteh Lagzi

Batch normalization dramatically increases the largest trainable depth of residual networks, and this benefit has been crucial to the empirical success of deep residual networks on a wide range of benchmarks. We show that this key benefit…

Machine Learning · Computer Science 2020-12-10 Soham De , Samuel L. Smith

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…

Machine Learning · Computer Science 2021-01-05 Qianli Liao , Tomaso Poggio

Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the…

Machine Learning · Statistics 2019-11-12 Talha Cihad Gulcu

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…

Machine Learning · Computer Science 2020-12-23 Kaixuan Huang , Yuqing Wang , Molei Tao , Tuo Zhao

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…

Computer Vision and Pattern Recognition · Computer Science 2018-11-27 Linan Zhang , Hayden Schaeffer

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…

Computer Vision and Pattern Recognition · Computer Science 2018-06-25 Francois Rousseau , Ronan Fablet

3D shape models that directly classify objects from 3D information have become more widely implementable. Current state of the art models rely on deep convolutional and inception models that are resource intensive. Residual neural networks…

Computer Vision and Pattern Recognition · Computer Science 2017-10-04 Varun Arvind , Anthony Costa , Marcus Badgeley , Samuel Cho , Eric Oermann

Deep Convolutional Neural Networks (CNNs) i.e. Residual Networks (ResNets) have been used successfully for many computer vision tasks, but are difficult to scale to 3D volumetric medical data. Memory is increasingly often the bottleneck…

Image and Video Processing · Electrical Eng. & Systems 2021-03-17 Kashu Yamazaki , Vidhiwar Singh Rathour , T. Hoang Ngan Le

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…

Machine Learning · Computer Science 2016-03-29 Sasha Targ , Diogo Almeida , Kevin Lyman