In distributed training, the communication cost due to the transmission of gradients
 or the parameters of the deep model is a major bottleneck in scaling up the number
 of processing nodes. To address this issue, we propose dithered quantization for
 the transmission of the stochastic gradients and show that training with Dithered
 Quantized Stochastic Gradients (DQSG) is similar to the training with unquantized
 SGs perturbed by an independent bounded uniform noise, in contrast to the other
 quantization methods where the perturbation depends on the gradients and hence,
 complicating the convergence analysis. We study the convergence of training
 algorithms using DQSG and the trade off between the number of quantization
 levels and the training time. Next, we observe that there is a correlation among the
 SGs computed by workers that can be utilized to further reduce the communication
 overhead without any performance loss. Hence, we develop a simple yet effective
 quantization scheme, nested dithered quantized SG (NDQSG), that can reduce the
 communication significantly without requiring the workers communicating extra
 information to each other. We prove that although NDQSG requires significantly
 less bits, it can achieve the same quantization variance bound as DQSG. Our
 simulation results confirm the effectiveness of training using DQSG and NDQSG
 in reducing the communication bits or the convergence time compared to the
 existing methods without sacrificing the accuracy of the trained model.
The paper proposes and analyzes two quantization schemes for communicating Stochastic Gradients in distributed learning which would reduce communication costs compare to the state of the art while maintaining the same accuracy.   The authors propose applying dithered quantization to the stochastic gradients computed through the training process, which improves quantization error and achieves superior results compared to baselines, and propose a nested scheme to reduce communication cost. Authors establish a connection between communication reduction in distributed optimization and dithered quantization and develops two new distributed training algorithms where communication overhead is significantly reduced.