We train deep residual networks with a stochastic variant of the nonlinear multigrid method MG/OPT. To build the multilevel hierarchy, we use the dynamical systems viewpoint specific to residual networks. We report significant speed-ups and additional robustness for training MNIST on deep residual networks. Our numerical experiments also indicate that multilevel training can be used as a pruning technique, as many of the auxiliary networks have accuracies comparable to the original network.
University of California, Los Angeles（加州大学洛杉矶分校）；Purdue University（普渡大学）
We propose a new bootstrap-based online algorithm for stochastic linear bandit problems. The key idea is to adopt residual bootstrap exploration, in which the agent estimates the next step reward by re-sampling the residuals of mean reward estimate. Our algorithm, residual bootstrap exploration for stochastic linear bandit (\texttt{LinReBoot}), estimates the linear reward from its re-sampling distribution and pulls the arm with the highest reward estimate. In particular, we contribute a theoretical framework to demystify residual bootstrap-based exploration mechanisms in stochastic linear band…
University of Science and Technology of China（中国科学技术大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Columbia University（哥伦比亚大学）
During the last few years, significant attention has been paid to the stochastic training of artificial neural networks, which is known as an effective regularization approach that helps improve the generalization capability of trained models. In this work, the method of modified equations is applied to show that the residual network and its variants with noise injection can be regarded as weak approximations of stochastic differential equations. Such observations enable us to bridge the stochastic training processes with the optimal control of backward Kolmogorov's equations. This not only of…
Broad stochastic configuration residual learning system for norm-convergent universal approximation
School of Control and Computer Engineering, North China Electric Power University（控制与计算机工程学院，华北电力大学）；School of Mathematics and Physics, North China Electric Power University（数学与物理学院，华北电力大学）；School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University（智能系统工程学院，中山大学深圳校区）
University of Oxford（牛津大学）；Instadeep Ltd（Instadeep有限公司）；University of Southern California（南加州大学）
We investigate the asymptotic properties of deep Residual networks (ResNets) as the number of layers increases. We first show the existence of scaling regimes for trained weights markedly different from those implicitly assumed in the neural ODE literature. We study the convergence of the hidden state dynamics in these scaling regimes, showing that one may obtain an ODE, a stochastic differential equation (SDE) or neither of these. In particular, our findings point to the existence of a diffusive regime in which the deep network limit is described by a class of stochastic differential equation…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；LIP6（巴黎第六大学计算机实验室）；Criteo AI Lab（Criteo人工智能实验室）
Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whos…
The University of Melbourne（墨尔本大学）；Indian Institute of Technology, Delhi（印度理工学院德里分校）
The ubiquitous adoption of Internet-of-Things (IoT) based applications has resulted in the emergence of the Fog computing paradigm, which allows seamlessly harnessing both mobile-edge and cloud resources. Efficient scheduling of application tasks in such environments is challenging due to constrained resource capabilities, mobility factors in IoT, resource heterogeneity, network hierarchy, and stochastic behaviors. xisting heuristics and Reinforcement Learning based approaches lack generalizability and quick adaptability, thus failing to tackle this problem optimally. They are also unable to u…
Large-scale machine learning models are often trained by parallel stochastic gradient descent algorithms. However, the communication cost of gradient aggregation and model synchronization between the master and worker nodes becomes the major obstacle for efficient learning as the number of workers and the dimension of the model increase. In this paper, we propose DORE, a DOuble REsidual compression stochastic gradient descent algorithm, to reduce over $95\%$ of the overall communication such that the obstacle can be immensely mitigated. Our theoretical analyses demonstrate that the proposed st…
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
University of Cambridge（剑桥大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Allen Institute（艾伦研究所）；University of Washington（华盛顿大学）；Cornell University（康奈尔大学）
Technical University of Munich（慕尼黑工业大学）；Imperial College London（伦敦帝国学院）
The training of neural networks with Differentially Private Stochastic Gradient Descent offers formal Differential Privacy guarantees but introduces accuracy trade-offs. In this work, we propose to alleviate these trade-offs in residual networks with Group Normalisation through a simple architectural modification termed ScaleNorm by which an additional normalisation layer is introduced after the residual block's addition operation. Our method allows us to further improve on the recently reported state-of-the art on CIFAR-10, achieving a top-1 accuracy of 82.5% (ε=8.0) when trained from scratch…
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…
mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations
CSE, University of Michigan, Ann Arbor, USA（计算机科学与工程系，密歇根大学，安娜堡，美国）；CCDS, Nanyang Technological University, Singapore（计算机科学与数据科学系，南洋理工大学，新加坡）；CBS-NTT Physics of Intelligence Program, Harvard University, Cambridge, USA（哈佛大学剑桥分校人工智能物理计划）；Physics of Artificial Intelligence Group, NTT Research Inc, USA（人工智能物理研究组，NTT研究公司，美国）
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 relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE liter…
Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very deep networks comes with its own set of challenges. The gradients can vanish, the forward flow often diminishes, and the training time can be painfully slow. To address these problems, we propose stochastic depth, a training procedure that enables the seemingly contradictory setup to train short networks and use deep networks at test time. We start with very de…
UT-Battelle, LLC（UT-巴特尔有限责任公司）；US Department of Energy (DOE)（美国能源部）
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 fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power and allows to control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet do…
Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration
Indian Institute of Technology Kharagpur（印度理工学院Khargapur分校）；Mohamed bin Zayed University of Artificial Intelligence（Mohamed bin Zayed人工智能大学）；Purdue University（普渡大学）
Università della Svizzera italiana（瑞士意大利语大学）；Euler Institute（欧拉研究所）
We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trust-region (RMTR) method, which operates in hybrid (stochastic-deterministic) settings by adaptively adjusting mini-batch sizes during the training. The multilevel hierarchy and the transfer operators are constructed by exploiting a dynamical system's viewpoint, which interprets forward propagation through the ResNet as a forward Euler discretization of an initial value problem. In contrast to traditional training appr…
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…
