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 low-rank gradient compressor 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.

Low-rank gradient compression methods, such as PowerSGD, have gained attention in communication-efficient distributed optimization. However, the convergence guarantees of PowerSGD remain unclear, particularly in stochastic settings. In this paper, we show that PowerSGD does not always converge to the optimal solution and provide a clear counterexample to support this finding. To address this, we introduce PowerSGD+, which periodically updates the projection subspace via singular value decomposition, ensuring that it remains aligned with the optimal subspace. We prove that PowerSGD+ converges under standard assumptions and validate its effectiveness through empirical evaluation on large language model tasks.

We thank the reviewers for their insightful comments and encouraging feedback. Reviewer 1 raises two concerns about speedups which we believe to be based on a misunderstanding. A 2 reduction in this metric seems significant. We will clarify this in the paper. Secondly, the reviewer suspects that Tables 6 and 7 show timings for the slower GLOO backend.

We propose LQ-SGD (Low-Rank Quantized Stochastic Gradient Descent), an efficient communication gradient compression algorithm designed for distributed training. LQ-SGD further develops on the basis of PowerSGD by incorporating the low-rank approximation and log-quantization techniques, which drastically reduce the communication overhead, while still ensuring the convergence speed of training and model accuracy. In addition, LQ-SGD and other compression-based methods show stronger resistance to gradient inversion than traditional SGD, providing a more robust and efficient optimization path for distributed learning systems. With the rapid development of learning models, distributed training has become a fundamental approach to improving model performance and scalability. However, these distributed training systems typically rely on numerous compute nodes working collaboratively, where the synchronization of model parameters and gradients introduces significant communication overhead.

Update: I have carefully read the authors' rebuttal. I have raised by score to 6 from 5 to reflect their clarification about Figure 3 and Table 6. It still seems that the speedups of the current formulation are often not of great practical significance, except for the language model which was able to give 2x wall clock speedup. As another reviewer noted, it is disappointing that the overall training time is not reported in the main paper, instead of the average batch time, as that makes it unclear whether latency times and other overheads between batches might be a significant concern. The author rebuttal notes that Appendix C shows time-to-accuracy, which would be good to mention in the main paper. But those results still appear mixed: for CIFAR10 SGD beats Rank1 and seems only competitive with Ranks 2,4, whereas for Language model all Ranks seem to convincingly beat SGD.

DL is the method used to accelerate the training of deep learning models by distributing training tasks to multiple computing nodes [1]. However, as data scales continue to grow, the complexity of model gradients increases accordingly, for example, consider the training of deep learning on ImageNet [2], which contains over 14 million labeled images and topics with approximately 22,000 categories, leading to constraints on communication efficiency [3]. Gradient compression aimed at reducing communication overhead during gradient transmission between multiple nodes which enhances system computational efficiency [4, 5, 6], thus this has emerged as an effective optimization technique in distributed learning, especially when training complex models to process large-scale data. Among various gradient compression techniques, PowerSGD [6] and Top-K SGD [7] have emerged as prominent solutions for their ability to substantially reduce communication costs while preserving scalability and model accuracy in large-scale distributed learning. These two algorithms are particularly suitable for our study as they represent fundamental approaches to gradient compression: PowerSGD uses low-rank approximation, while TopKSGD leverages sparsification through threshold quantization. Both techniques are widely recognized for their practical effectiveness, especially when combined, to varying extents, with advanced features such as error feedback, warm start, all-reduce, making them ideal candidates of compressed SGD for assessing privacy risks in distributed deep learning systems.

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 low-rank gradient compressor 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.

Data-parallel distributed training of deep neural networks (DNN) has gained very widespread adoption, but can still experience communication bottlenecks. To address this issue, entire families of compression mechanisms have been developed, including quantization, sparsification, and low-rank approximation, some of which are seeing significant practical adoption. Despite this progress, almost all known compression schemes apply compression uniformly across DNN layers, although layers are heterogeneous in terms of parameter count and their impact on model accuracy. In this work, we provide a general framework for adapting the degree of compression across the model's layers dynamically during training, improving the overall compression, while leading to substantial speedups, without sacrificing accuracy. Our framework, called L-GreCo, is based on an adaptive algorithm, which automatically picks the optimal compression parameters for model layers guaranteeing the best compression ratio while satisfying an error constraint. Extensive experiments over image classification and language modeling tasks shows that L-GreCo is effective across all existing families of compression methods, and achieves up to 2.5 training speedup and up to 5 compression improvement over efficient implementations of existing approaches, while recovering full accuracy. Moreover, L-GreCo is complementary to existing adaptive algorithms, improving their compression ratio by 50% and practical throughput by 66%. An anonymized implementation is available at https://github.com/LGrCo/L-GreCo. The massive growth in model and dataset sizes for deep The second is sparsification (Strom, 2015; Dryden et al., learning has made distribution a standard approach to training. The third and most recent approach each of which computes stochastic gradients over their data, is low-rank approximation (Wang et al., 2018; Vogels et al., and then averages the workers' gradients in a synchronous 2019), which leverages the low-rank structure of gradient step.

While differential privacy and gradient compression are separately well-researched topics in machine learning, the study of interaction between these two topics is still relatively new. We perform a detailed empirical study on how the Gaussian mechanism for differential privacy and gradient compression jointly impact test accuracy in deep learning. The existing literature in gradient compression mostly evaluates compression in the absence of differential privacy guarantees, and demonstrate that sufficiently high compression rates reduce accuracy. Similarly, existing literature in differential privacy evaluates privacy mechanisms in the absence of compression, and demonstrates that sufficiently strong privacy guarantees reduce accuracy. In this work, we observe while gradient compression generally has a negative impact on test accuracy in non-private training, it can sometimes improve test accuracy in differentially private training. Specifically, we observe that when employing aggressive sparsification or rank reduction to the gradients, test accuracy is less affected by the Gaussian noise added for differential privacy. These observations are explained through an analysis how differential privacy and compression effects the bias and variance in estimating the average gradient. We follow this study with a recommendation on how to improve test accuracy under the context of differentially private deep learning and gradient compression. We evaluate this proposal and find that it can reduce the negative impact of noise added by differential privacy mechanisms on test accuracy by up to 24.6%, and reduce the negative impact of gradient sparsification on test accuracy by up to 15.1%.