  We study gradient compression methods to alleviate the communication
bottleneck in data-parallel distributed optimization. Despite the significant
attention received, current compression schemes either do not scale well or
fail to achieve the target test accuracy. We propose a new low-rank gradient
compressor based on power iteration that can i) compress gradients rapidly, ii)
efficiently aggregate the compressed gradients using all-reduce, and iii)
achieve test performance on par with SGD. The proposed algorithm is the only
method evaluated that achieves consistent wall-clock speedups when benchmarked
against regular SGD with an optimized communication backend. We demonstrate
reduced training times for convolutional networks as well as LSTMs on common
datasets. Our code is available at https://github.com/epfml/powersgd.
