Compressed communication, in the form of sparsification or quantization of stochastic gradients, is employed to reduce communication costs in distributed data-parallel training of deep neural networks. However, there exists a discrepancy between theory and practice: while theoretical analysis of most existing compression methods assumes compression is applied to the gradients of the entire model, many practical implementations operate individually on the gradients of each layer of the model. In this paper, we prove that layer-wise compression is, in theory, better, because the convergence rate is upper bounded by that of entire-model compression for a wide range of biased and unbiased compression methods. However, despite the theoretical bound, our experimental study of six well-known methods shows that convergence, in practice, may or may not be better, depending on the actual trained model and compression ratio. Our findings suggest that it would be advantageous for deep learning frameworks to include support for both layer-wise and entire-model compression.

通过实验和理论分析，本文表明在深度神经网络的分布式数据并行训练中，面向单个层的压缩比面向整个模型的压缩方式更好，但实验也显示，具体训练模型和压缩率都可能导致实际收敛率的变化。因此，本文建议深度学习框架应支持面向单个层和整个模型的压缩方式。

分布式深度学习压缩通信的理论分析与实际实现之间的差异