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A Practical Layer-Parallel Training Algorithm for Residual Networks

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 Added by Qi Sun
 Publication date 2020
and research's language is English




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Gradient-based algorithms for training ResNets typically require a forward pass of the input data, followed by back-propagating the objective gradient to update parameters, which are time-consuming for deep ResNets. To break the dependencies between modules in both the forward and backward modes, auxiliary-variable methods such as the penalty and augmented Lagrangian (AL) approaches have attracted much interest lately due to their ability to exploit layer-wise parallelism. However, we observe that large communication overhead and lacking data augmentation are two key challenges of these methods, which may lead to low speedup ratio and accuracy drop across multiple compute devices. Inspired by the optimal control formulation of ResNets, we propose a novel serial-parallel hybrid training strategy to enable the use of data augmentation, together with downsampling filters to reduce the communication cost. The proposed strategy first trains the network parameters by solving a succession of independent sub-problems in parallel and then corrects the network parameters through a full serial forward-backward propagation of data. Such a strategy can be applied to most of the existing layer-parallel training methods using auxiliary variables. As an example, we validate the proposed strategy using penalty and AL methods on ResNet and WideResNet across MNIST, CIFAR-10 and CIFAR-100 datasets, achieving significant speedup over the traditional layer-serial training methods while maintaining comparable accuracy.



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Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be interpreted as forward Euler discretizations of a nonlinear initial value problem whose time-dependent control variables represent the weights of the neural network. Hence, training a ResNet can be cast as an optimal control problem of the associated dynamical system. For similar time-dependent optimal control problems arising in engineering applications, parallel-in-time methods have shown notable improvements in scalability. This paper demonstrates the use of those techniques for efficient and effective training of ResNets. The proposed algorithms replace the classical (sequential) forward and backward propagation through the network layers by a parallel nonlinear multigrid iteration applied to the layer domain. This adds a new dimension of parallelism across layers that is attractive when training very deep networks. From this basic idea, we derive multiple layer-parallel methods. The most efficient version employs a simultaneous optimization approach where updates to the network parameters are based on inexact gradient information in order to speed up the training process. Using numerical examples from supervised classification, we demonstrate that the new approach achieves similar training performance to traditional methods, but enables layer-parallelism and thus provides speedup over layer-serial methods through greater concurrency.
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