In this work we apply model averaging to parallel training of deep neural network (DNN). Parallelization is done in a model averaging manner. Data is partitioned and distributed to different nodes for local model updates, and model averaging across nodes is done every few minibatches. We use multiple GPUs for data parallelization, and Message Passing Interface (MPI) for communication between nodes, which allows us to perform model averaging frequently without losing much time on communication. We investigate the effectiveness of Natural Gradient Stochastic Gradient Descent (NG-SGD) and Restricted Boltzmann Machine (RBM) pretraining for parallel training in model-averaging framework, and explore the best setups in term of different learning rate schedules, averaging frequencies and minibatch sizes. It is shown that NG-SGD and RBM pretraining benefits parameter-averaging based model training. On the 300h Switchboard dataset, a 9.3 times speedup is achieved using 16 GPUs and 17 times speedup using 32 GPUs with limited decoding accuracy loss.
Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and describe two ways in which the frequency of averaging affects convergence. For convex objectives, we show the benefit of frequent averaging depends on the gradient variance envelope. For non-convex objectives, we illustrate that this benefit depends on the presence of multiple globally optimal points. We complement our findings with multicore experiments on both …
Effective regularisation during training can mean the difference between success and failure for deep neural networks. Recently, dither has been suggested as alternative to dropout for regularisation during batch-averaged stochastic gradient descent (SGD). In this article, we show that these methods fail without batch averaging and we introduce a new, parallel regularisation method that may be used without batch averaging. Our results for parallel-regularised non-batch-SGD are substantially better than what is possible with batch-SGD. Furthermore, our results demonstrate that dither and dropou…
We describe the neural-network training framework used in the Kaldi speech recognition toolkit, which is geared towards training DNNs with large amounts of training data using multiple GPU-equipped or multi-core machines. In order to be as hardware-agnostic as possible, we needed a way to use multiple machines without generating excessive network traffic. Our method is to average the neural network parameters periodically (typically every minute or two), and redistribute the averaged parameters to the machines for further training. Each machine sees different data. By itself, this method does …
In distributed training of deep neural networks, parallel mini-batch SGD is widely used to speed up the training process by using multiple workers. It uses multiple workers to sample local stochastic gradient in parallel, aggregates all gradients in a single server to obtain the average, and update each worker's local model using a SGD update with the averaged gradient. Ideally, parallel mini-batch SGD can achieve a linear speed-up of the training time (with respect to the number of workers) compared with SGD over a single worker. However, such linear scalability in practice is significantly l…
Microsoft Research（微软研究院）；University of Washington（华盛顿大学）；Stanford University（斯坦福大学）
This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estimate and for parallelizing SGD and (2) tail-averaging, a method involving averaging the final few iterates of SGD to decrease the variance in SGD's final iterate. This work presents non-asymptotic excess risk bounds for these schemes for the stochastic approximation problem of leas…
The state-of-the-art deep learning algorithms rely on distributed training systems to tackle the increasing sizes of models and training data sets. Minibatch stochastic gradient descent (SGD) algorithm requires workers to halt forward/back propagations, to wait for gradients aggregated from all workers, and to receive weight updates before the next batch of tasks. This synchronous execution model exposes the overheads of gradient/weight communication among a large number of workers in a distributed training system. We propose a new SGD algorithm, DaSGD (Local SGD with Delayed Averaging), which…
Facebook AI Research（脸书人工智能研究院）；Princeton University（普林斯顿大学）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）
First-order stochastic optimization methods are currently the most widely used class of methods for training deep neural networks. However, the choice of the optimizer has become an ad-hoc rule that can significantly affect the performance. For instance, SGD with momentum (SGD+M) is typically used in computer vision (CV) and Adam is used for training transformer models for Natural Language Processing (NLP). Using the wrong method can lead to significant performance degradation. Inspired by the dual averaging algorithm, we propose Modernized Dual Averaging (MDA), an optimizer that is able to pe…
Hierarchical Weight Averaging for Deep Neural Networks
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Pengcheng Laboratory（鹏城实验室）；Institute of High Performance Computing, Agency for Science, Technology and Research（新加坡科技研究局高性能计算研究所）
Institute of Evaluation and Assessment Research, Academy of Military Science（军事科学院评估论证研究中心）；Command and Control Engineering College, Army Engineering University（陆军工程大学指挥控制工程学院）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of sufficient convergence analysis for strongly convex optimization. Typically, the convergence about the last iterate of gradient descent methods, which is referred to as individual convergence, fails to attain its optimality due to the existence of logarithmic factor. In order to remove this factor, we first develop gradient descent averaging (GDA), which is …
Georgia Institute of Technology（佐治亚理工学院）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Reducing communication in training large-scale machine learning applications on distributed platform is still a big challenge. To address this issue, we propose a distributed hierarchical averaging stochastic gradient descent (Hier-AVG) algorithm with infrequent global reduction by introducing local reduction. As a general type of parallel SGD, Hier-AVG can reproduce several popular synchronous parallel SGD variants by adjusting its parameters. We show that Hier-AVG with infrequent global reduction can still achieve standard convergence rate for non-convex optimization problems. In addition, w…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Google Inc.（谷歌公司）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
Decentralized SGD is an emerging training method for deep learning known for its much less (thus faster) communication per iteration, which relaxes the averaging step in parallel SGD to inexact averaging. The less exact the averaging is, however, the more the total iterations the training needs to take. Therefore, the key to making decentralized SGD efficient is to realize nearly-exact averaging using little communication. This requires a skillful choice of communication topology, which is an under-studied topic in decentralized optimization. In this paper, we study so-called exponential graph…
Communication overhead hinders the scalability of large-scale distributed training. Gossip SGD, where each node averages only with its neighbors, is more communication-efficient than the prevalent parallel SGD. However, its convergence rate is reversely proportional to quantity $1-β$ which measures the network connectivity. On large and sparse networks where $1-β\to 0$, Gossip SGD requires more iterations to converge, which offsets against its communication benefit. This paper introduces Gossip-PGA, which adds Periodic Global Averaging into Gossip SGD. Its transient stage, i.e., the iterations…
Georgia Institute of Technology（佐治亚理工学院）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Despite their popularity, the practical performance of asynchronous stochastic gradient descent methods (ASGD) for solving large scale machine learning problems are not as good as theoretical results indicate. We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG. We establish the convergence results of K-AVG for nonconvex objectives and explain why the K-step delay is necessary and leads to better performance than traditional parallel stochastic gradient descent which is a special case of K-AVG with $K=1$. We also show that K-AVG scales …
Massachusetts Institute of Technology, Lincoln Laboratory（麻省理工学院林肯实验室）
Multiple techniques for producing calibrated predictive probabilities using deep neural networks in supervised learning settings have emerged that leverage approaches to ensemble diverse solutions discovered during cyclic training or training from multiple random starting points (deep ensembles). However, only a limited amount of work has investigated the utility of exploring the local region around each diverse solution (posterior mode). Using three well-known deep architectures on the CIFAR-10 dataset, we evaluate several simple methods for exploring local regions of the weight space with re…
We consider speeding up stochastic gradient descent (SGD) by parallelizing it across multiple workers. We assume the same data set is shared among $N$ workers, who can take SGD steps and coordinate with a central server. While it is possible to obtain a linear reduction in the variance by averaging all the stochastic gradients at every step, this requires a lot of communication between the workers and the server, which can dramatically reduce the gains from parallelism. The Local SGD method, proposed and analyzed in the earlier literature, suggests machines should make many local steps between…
Courant Institute, NYU（纽约大学柯朗研究所）；Center for Data Science, NYU（纽约大学数据科学中心）；Facebook AI Research（脸书人工智能研究院）
We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of commun…
Momentum methods are now used pervasively within the machine learning community for training non-convex models such as deep neural networks. Empirically, they out perform traditional stochastic gradient descent (SGD) approaches. In this work we develop a Lyapunov analysis of SGD with momentum (SGD+M), by utilizing a equivalent rewriting of the method known as the stochastic primal averaging (SPA) form. This analysis is much tighter than previous theory in the non-convex case, and due to this we are able to give precise insights into when SGD+M may out-perform SGD, and what hyper-parameter sche…
Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative solutions into a single solution, is still under-explored. While some increasingly weighted averaging schemes have been considered in the literature, existing works are mostly restricted to strongly convex objective functions and the convergence of optimization error. It remains unclear how these averaging schemes affect the convergence of {\it both optimiza…
Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data analysis. We propose in this work a new framework to carry out averaging of these datasets, with the goal of synthesizing a representative template trajectory from multiple trajectories. We show that this requires addressing three sources of invariance: shifts in time, space, and total population size (or mass/amplitude). Here we draw inspiration from dynamic tim…
Although deep neural networks (DNN) are able to scale with direct advances in computational power (e.g., memory and processing speed), they are not well suited to exploit the recent trends for parallel architectures. In particular, gradient descent is a sequential process and the resulting serial dependencies mean that DNN training cannot be parallelized effectively. Here, we show that a DNN may be replicated over a massive parallel architecture and used to provide a cumulative sampling of local solution space which results in rapid and robust learning. We introduce a complimentary convolution…
NTT DATA Mathematical Systems Inc.（NTT DATA 数理系统公司）；The University of Tokyo（东京大学）
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient estimate and can easily make good use of parallel computing. The core of our proposed method is the incorporation of our new "double acceleration" technique and variance reduction technique. We theoretically analyze our proposed method and show that our method much improves the min…
The University of Iowa（爱荷华大学）；Augusta University（奥古斯塔大学）
Stochastic Gradient Descent (SGD) is the key learning algorithm for many machine learning tasks. Because of its computational costs, there is a growing interest in accelerating SGD on HPC resources like GPU clusters. However, the performance of parallel SGD is still bottlenecked by the high communication costs even with a fast connection among the machines. A simple approach to alleviating this problem, used in many existing efforts, is to perform communication every few iterations, using a constant averaging period. In this paper, we show that the optimal averaging period in terms of converge…
Facebook AI Research（Facebook人工智能研究院）；McGill University（麦吉尔大学）；University of Edinburgh（爱丁堡大学）
Distributed data-parallel algorithms aim to accelerate the training of deep neural networks by parallelizing the computation of large mini-batch gradient updates across multiple nodes. Approaches that synchronize nodes using exact distributed averaging (e.g., via AllReduce) are sensitive to stragglers and communication delays. The PushSum gossip algorithm is robust to these issues, but only performs approximate distributed averaging. This paper studies Stochastic Gradient Push (SGP), which combines PushSum with stochastic gradient updates. We prove that SGP converges to a stationary point of s…
We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple models computed independently and in parallel. The resulting models generalize equally well as those trained with small mini-batches but are produced in a substantially shorter time. We demonstrate the reduction in training time and the good generalization performance of the resulting models on the computer vision datasets CIFAR10, CIFAR100, and ImageNet.
Cornell University（康奈尔大学）；Higher School of Economics（高等经济学院）；Samsung-HSE Laboratory（三星-高等经济学院实验室）；Samsung AI Center in Moscow（莫斯科三星人工智能中心）；Lomonosov Moscow State University（莫斯科国立大学（罗蒙诺索夫莫斯科国立大学））
Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conventional training. We also show that this Stochastic Weight Averaging (SWA) procedure finds much flatter solutions than SGD, and approximates the recent Fast Geometric Ensembling (FGE) approach with a single model. Using SWA we achieve notable improvement in test accuracy over co…
Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently provided an equivalent convex training problem. However, extending this result to deeper networks remains to be an open problem. In this paper, we prove that the duality gap for deeper linear networks with vector outputs is non-zero. In contrast, we show that the zero duality gap can be obtained by stacking standard deep networks in parallel, which we call a paral…
This paper describes neural-fortran, a parallel Fortran framework for neural networks and deep learning. It features a simple interface to construct feed-forward neural networks of arbitrary structure and size, several activation functions, and stochastic gradient descent as the default optimization algorithm. Neural-fortran also leverages the Fortran 2018 standard collective subroutines to achieve data-based parallelism on shared- or distributed-memory machines. First, I describe the implementation of neural networks with Fortran derived types, whole-array arithmetic, and collective sum and b…
There is significant recent interest to parallelize deep learning algorithms in order to handle the enormous growth in data and model sizes. While most advances focus on model parallelization and engaging multiple computing agents via using a central parameter server, aspect of data parallelization along with decentralized computation has not been explored sufficiently. In this context, this paper presents a new consensus-based distributed SGD (CDSGD) (and its momentum variant, CDMSGD) algorithm for collaborative deep learning over fixed topology networks that enables data parallelization as w…
New York University（纽约大学）；Samsung AI Center Moscow（三星莫斯科人工智能中心）；National Research University Higher School of Economics（国立研究型大学高等经济学院）
We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sa…
Northwestern Polytechnical University（西北工业大学）；Tencent AI Lab（腾讯人工智能实验室）
Deep learning models (DLMs) are state-of-the-art techniques in speech recognition. However, training good DLMs can be time consuming especially for production-size models and corpora. Although several parallel training algorithms have been proposed to improve training efficiency, there is no clear guidance on which one to choose for the task in hand due to lack of systematic and fair comparison among them. In this paper we aim at filling this gap by comparing four popular parallel training algorithms in speech recognition, namely asynchronous stochastic gradient descent (ASGD), blockwise model…
Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious patterns or biases that do not actually exist. Another complication is introduced if the number of features varies between each set. We propose convolutional deep averaging networks (CDANs) for classifying and learning representations of datasets whose instances comprise variable-size, unordered feature sets. CDANs are efficient, permutation-invariant, and cap…
In recent years, neural networks (NNs) have made giant leaps in a wide variety of domains. NNs are often referred to as black box algorithms due to how little we can explain their empirical success. Our foundational research seeks to explain why neural networks generalize. A recent advancement derived a mutual information measure for explaining the performance of deep NNs through a sequence of increasingly complex functions. We show deep NNs learn a series of boosted classifiers whose generalization is popularly attributed to self-averaging over an increasing number of interpolating sub-classi…
Designing a deep neural network (DNN) with good generalization capability is a complex process especially when the weights are severely quantized. Model averaging is a promising approach for achieving the good generalization capability of DNNs, especially when the loss surface for training contains many sharp minima. We present a new quantized neural network optimization approach, stochastic quantized weight averaging (SQWA), to design low-precision DNNs with good generalization capability using model averaging. The proposed approach includes (1) floating-point model training, (2) direct quant…
Florida International University（佛罗里达国际大学）；Gladstone Institutes（格莱斯顿研究所）
Several neurodegenerative diseases involve the accumulation of cellular DNA damage. Comet assays are a popular way of estimating the extent of DNA damage. Current literature on the use of deep learning to quantify DNA damage presents an empirical approach to hyper-parameter optimization and does not include uncertainty estimates. Deep ensemble averaging is a standard approach to estimating uncertainty but it requires several iterations of network training, which makes it time-consuming. Here we present an approach to quantify the extent of DNA damage that combines deep learning with a rigorous…
Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；University of Bonn（波恩大学）；Volkswagen Group Research（大众集团研究院）
We propose an efficient protocol for decentralized training of deep neural networks from distributed data sources. The proposed protocol allows to handle different phases of model training equally well and to quickly adapt to concept drifts. This leads to a reduction of communication by an order of magnitude compared to periodically communicating state-of-the-art approaches. Moreover, we derive a communication bound that scales well with the hardness of the serialized learning problem. The reduction in communication comes at almost no cost, as the predictive performance remains virtually uncha…
Parallelization framework has become a necessity to speed up the training of deep neural networks (DNN) recently. Such framework typically employs the Model Average approach, denoted as MA-DNN, in which parallel workers conduct respective training based on their own local data while the parameters of local models are periodically communicated and averaged to obtain a global model which serves as the new start of local models. However, since DNN is a highly non-convex model, averaging parameters cannot ensure that such global model can perform better than those local models. To tackle this prob…
Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on prior work and argue that a multi-headed network structure we name HydraNet provides better calibrated uncertainty estimates than methods that rely on stochastic forward passes. Second, we extend HydraNet to targets that belong to the rotation group, SO(3), by regressing unit quaternions and using the tools of rotation averaging and uncertainty injection on…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）
Recent advances in deep learning have achieved impressive gains in classification accuracy on a variety of types of data, including images and text. Despite these gains, however, concerns have been raised about the calibration, robustness, and interpretability of these models. In this paper we propose a simple way to modify any conventional deep architecture to automatically provide more transparent explanations for classification decisions, as well as an intuitive notion of the credibility of each prediction. Specifically, we draw on ideas from nonparametric kernel regression, and propose to …
Smart buildings are the need of the day with increasing demand-supply ratios and deficiency to generate considerably. In any modern non-industrial infrastructure, these demands mainly comprise of thermostatically controlled loads (TCLs), which can be manoeuvred. TCL loads like air-conditioner, heater, refrigerator, are ubiquitous, and their operating times can be controlled to achieve desired aggregate power. This power aggregation, in turn, helps achieve load management targets and thereby serve as ancillary service (AS) to the power grid. In this work, a distributed averaging protocol is use…
Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels. We leverage this observation to study representation learning in these networks, allowing us to connect limiting results obtained in previous studies within a unified framework. In total, these results advance o…
Trainable Weight Averaging: Accelerating Training and Improving Generalization
Shanghai Jiao Tong University（上海交通大学）；KU Leuven（鲁汶大学）；National Taiwan University（台湾大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
University of Berkeley（加州大学伯克利分校）；Google Research（谷歌研究院）；Graphcore Research（Graphcore研究院）；Graphcore
Deep learning models trained on large data sets have been widely successful in both vision and language domains. As state-of-the-art deep learning architectures have continued to grow in parameter count so have the compute budgets and times required to train them, increasing the need for compute-efficient methods that parallelize training. Two common approaches to parallelize the training of deep networks have been data and model parallelism. While useful, data and model parallelism suffer from diminishing returns in terms of compute efficiency for large batch sizes. In this paper, we investig…
WASH: Train your Ensemble with Communication-Efficient Weight Shuffling, then Average
ISIR - Sorbonne Université（ISIR - 索邦大学）；Mila（米拉研究所）；Concordia University（康考迪亚大学）；École de technologie supérieure（高等技术学院）；Center for Computational Mathematics（计算数学中心）；Flatiron Institute（弗拉特iron研究所）
National University of Defense Technology（国防科技大学）；Sun Yat-Sen University（中山大学）；Queen Mary University of London（伦敦玛丽女王大学）
Valuable training data is often owned by independent organizations and located in multiple data centers. Most deep learning approaches require to centralize the multi-datacenter data for performance purpose. In practice, however, it is often infeasible to transfer all data to a centralized data center due to not only bandwidth limitation but also the constraints of privacy regulations. Model averaging is a conventional choice for data parallelized training, but its ineffectiveness is claimed by previous studies as deep neural networks are often non-convex. In this paper, we argue that model av…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Naver；AITRICS
Ensembles of deep neural networks have demonstrated superior performance, but their heavy computational cost hinders applying them for resource-limited environments. It motivates distilling knowledge from the ensemble teacher into a smaller student network, and there are two important design choices for this ensemble distillation: 1) how to construct the student network, and 2) what data should be shown during training. In this paper, we propose a weight averaging technique where a student with multiple subnetworks is trained to absorb the functional diversity of ensemble teachers, but then th…
Deep Neural Networks (DNNs) are becoming an important tool in modern computing applications. Accelerating their training is a major challenge and techniques range from distributed algorithms to low-level circuit design. In this survey, we describe the problem from a theoretical perspective, followed by approaches for its parallelization. We present trends in DNN architectures and the resulting implications on parallelization strategies. We then review and model the different types of concurrency in DNNs: from the single operator, through parallelism in network inference and training, to distri…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；University of Michigan（密歇根大学）
Federated learning allows edge devices to collaboratively learn a shared model while keeping the training data on device, decoupling the ability to do model training from the need to store the data in the cloud. We propose Federated matched averaging (FedMA) algorithm designed for federated learning of modern neural network architectures e.g. convolutional neural networks (CNNs) and LSTMs. FedMA constructs the shared global model in a layer-wise manner by matching and averaging hidden elements (i.e. channels for convolution layers; hidden states for LSTM; neurons for fully connected layers) wi…
