PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization (1905.13727v3)

Abstract: 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.

• The paper introduces a novel low-rank gradient compressor that uses power iteration to efficiently approximate gradients in distributed optimization.
• The paper demonstrates significant speedups, reducing communication time by 54% to 90% and overall training time by up to 55%.
• Methodological innovations like linear compression and error feedback enable scalable all-reduce aggregation while maintaining test accuracy comparable to standard SGD.

Review of "PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization"

This paper presents PowerSGD, a method for gradient compression that aims to alleviate the communication bottleneck in distributed optimization tasks. The authors address the limitations of existing compression schemes which either do not scale efficiently or fail to achieve desired test accuracies. PowerSGD introduces a novel low-rank gradient compressor based on power iteration that allows for rapid gradient compression, efficient aggregation using all-reduce, and maintains test performance comparable to standard Stochastic Gradient Descent (SGD).

Core Contributions

The authors identify critical properties for scalable gradient compression:

• Linearity of Compression: This property ensures that gradient messages can be hierarchical added using all-reduce, a more efficient communication method compared to all-gather operations.
• Error Feedback: Utilization of error feedback enhances both convergence and generalization, allowing PowerSGD to employ biased compressors successfully.
• Low-Rank Approximation: By using subspace iteration techniques for low-rank updates, the method can handle aggressive compression without sacrificing performance quality.

Numerical Performance

PowerSGD demonstrated significant wall-clock speedups over uncompressed SGD. Benchmarked in a 16-GPU environment, PowerSGD reduced communication time drastically—by 54% for a convolutional network on Cifar10 and by 90% for an LSTM on the Wikitext-2 dataset. This led to a reduction in total training time by 24% and 55% respectively for these models.

Methodological Insights

The methodology focuses on efficiently compressing gradients through linear operations, allowing for the use of scalable all-reduce aggregation. The single-step subspace power iteration efficiently approximates gradient matrices without costly matrix decompositions, aided by a warm-start strategy to maintain approximation quality across iterations.

Implications and Future Directions

Practically, PowerSGD moves closer to making gradient compression a viable component of large-scale distributed training frameworks. It highlights the potential for further optimization in scenarios where communication is a primary bottleneck. Theoretically, it contributes insights into low-rank characteristics of gradients which may influence regularization and generalization in deep learning models.

Moving forward, PowerSGD could be adapted for more extensive systems with thousands of nodes or integrated into mixed-precision training regimes to further reduce computational overhead. Evaluating its utility in varied network architectures and resource-constrained settings represents another avenue for exploration.

This paper provides a substantial contribution to distributed learning, presenting both a robust theoretical foundation and compelling empirical results. The methods introduced here are likely to influence future developments in communication-efficient machine learning.