期刊
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
卷 2, 期 1, 页码 1-23出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1247620
关键词
deep learning; residual networks; supervised learning; optimal control; layer-parallelization; parallel-in-time; simultaneous optimization
资金
- U.S. National Science Foundation [DMS 1522599, DMS 1751636]
- Sandia National Laboratories
- U.S. Department of Energy's National Nuclear Security Administration [DE-NA0003525]
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 with 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 a training performance similar to that of traditional methods, but enables layer-parallelism and thus provides speedup over layer-serial methods through greater concurrency.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据