  Communication overhead has become one of the major bottlenecks in the
distributed training of deep neural networks. To alleviate the concern, various
gradient compression methods have been proposed, and sign-based algorithms are
of surging interest. However, SIGNSGD fails to converge in the presence of data
heterogeneity, which is commonly observed in the emerging federated learning
(FL) paradigm. Error feedback has been proposed to address the non-convergence
issue. Nonetheless, it requires the workers to locally keep track of the
compression errors, which renders it not suitable for FL since the workers may
not participate in the training throughout the learning process. In this paper,
we propose a magnitude-driven sparsification scheme, which addresses the
non-convergence issue of SIGNSGD while further improving communication
efficiency. Moreover, the local update scheme is further incorporated to
improve the learning performance, and the convergence of the proposed method is
established. The effectiveness of the proposed scheme is validated through
experiments on Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets.
