Understanding Top-k Sparsification in Distributed Deep Learning
Distributed stochastic gradient descent (SGD) algorithms are widely deployed in training large-scale deep learning models, while the communication overhead among workers becomes the new system bottleneck. Recently proposed gradient sparsification techniques, especially Top- sparsification with error compensation (TopK-SGD), can significantly reduce the communication traffic without obvious impact on the model accuracy. Some theoretical studies have been carried out to analyze the convergence property of TopK-SGD. However, existing studies do not dive into the details of Top- operator in gradient sparsification and use relaxed bounds (e.g., exact bound of Random- ) for analysis; hence the derived results cannot well describe the real convergence performance of TopK-SGD. To this end, we first study the gradient distributions of TopK-SGD during training process through extensive experiments. We then theoretically derive a tighter bound for the Top- operator. Finally, we exploit the property of gradient distribution to propose an approximate top- selection algorithm, which is computing-efficient for GPUs, to improve the scaling efficiency of TopK-SGD by significantly reducing the computing overhead.
Top-k algorithm is a gradient sparsification method which gains its popularity to train deep networks due to its high compression ratio. However due to its computation overhead, it is not efficient on GPUs. This paper performs empirical study on the distribution of the gradients when training various deep networks, and provides a Gaussian approximation analysis to improve the convergence of the top-k algorithm. Further, the paper proposes to use a Gaussian-k algorithm to perform similar gradient sparsification with a much lower computational cost without losing much convergence accuracy compared to Dense-SGD. However, the theoretical result seems to me overstated in the sense that it lacks mathematical rigor in the proof and is not clear how much insights it brings to understand better why top-k sparsification algorithms work well in deep learning (Figure 5 shows that the bound is still too tight). It is written after Equation (6) that “One can easily prove that ? is convex and it is always less than the reference line (y = ?i/d + 1) if u follows bell shaped distributions as illustrated”, however it is not clear me in what sense this is true. The u are random variables, therefore ? is a curve which depends their realizations, hence it is a random curve. Or maybe it holds when d goes to infinity? The numerical results are specific with k = 0.001d, which makes it hard to see if the Gaussian-k algorithm would still work using different k/d ratio. As shown in Figure 2, some of the histograms of u^1_t are quite sparse (these plots are hard to read for different iterations, maybe use cdf instead and perform statistical test to check how close to Gaussian distributions), therefore in some of these cases the Gaussian approximation may be poor. It is worth further investigation of the robustness of this algorithm as a replacement of the top-k algorithm.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Understanding Top-k Sparsification in Distributed Deep Learning
Distributed stochastic gradient descent (SGD) algorithms are widely deployed in training large-scale deep learning models, while the communication overhead among workers becomes the new system bottleneck. Recently proposed gradient sparsification techniques, especially Top- sparsification with error compensation (TopK-SGD), can significantly reduce the communication traffic without obvious impact on the model accuracy. Some theoretical studies have been carried out to analyze the convergence property of TopK-SGD. However, existing studies do not dive into the details of Top- operator in gradient sparsification and use relaxed bounds (e.g., exact bound of Random- ) for analysis; hence the derived results cannot well describe the real convergence performance of TopK-SGD. To this end, we first study the gradient distributions of TopK-SGD during training process through extensive experiments. We then theoretically derive a tighter bound for the Top- operator. Finally, we exploit the property of gradient distribution to propose an approximate top- selection algorithm, which is computing-efficient for GPUs, to improve the scaling efficiency of TopK-SGD by significantly reducing the computing overhead.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



Top-k algorithm is a gradient sparsification method which gains its popularity to train deep networks due to its high compression ratio. However due to its computation overhead, it is not efficient on GPUs. This paper performs empirical study on the distribution of the gradients when training various deep networks, and provides a Gaussian approximation analysis to improve the convergence of the top-k algorithm. Further, the paper proposes to use a Gaussian-k algorithm to perform similar gradient sparsification with a much lower computational cost without losing much convergence accuracy compared to Dense-SGD. However, the theoretical result seems to me overstated in the sense that it lacks mathematical rigor in the proof and is not clear how much insights it brings to understand better why top-k sparsification algorithms work well in deep learning (Figure 5 shows that the bound is still too tight). It is written after Equation (6) that “One can easily prove that ? is convex and it is always less than the reference line (y = ?i/d + 1) if u follows bell shaped distributions as illustrated”, however it is not clear me in what sense this is true. The u are random variables, therefore ? is a curve which depends their realizations, hence it is a random curve. Or maybe it holds when d goes to infinity? The numerical results are specific with k = 0.001d, which makes it hard to see if the Gaussian-k algorithm would still work using different k/d ratio. As shown in Figure 2, some of the histograms of u^1_t are quite sparse (these plots are hard to read for different iterations, maybe use cdf instead and perform statistical test to check how close to Gaussian distributions), therefore in some of these cases the Gaussian approximation may be poor. It is worth further investigation of the robustness of this algorithm as a replacement of the top-k algorithm.
assistant
Top-k algorithm is a gradient sparsification method which gains its popularity to train deep networks due to its high compression ratio. However due to its computation overhead, it is not efficient on GPUs. This paper performs empirical study on the distribution of the gradients when training various deep networks, and provides a Gaussian approximation analysis to improve the convergence of the top-k algorithm. Further, the paper proposes to use a Gaussian-k algorithm to perform similar gradient sparsification with a much lower computational cost without losing much convergence accuracy compared to Dense-SGD. However, the theoretical result seems to me overstated in the sense that it lacks mathematical rigor in the proof and is not clear how much insights it brings to understand better why top-k sparsification algorithms work well in deep learning (Figure 5 shows that the bound is still too tight). It is written after Equation (6) that “One can easily prove that ? is convex and it is always less than the reference line (y = ?i/d + 1) if u follows bell shaped distributions as illustrated”, however it is not clear me in what sense this is true. The u are random variables, therefore ? is a curve which depends their realizations, hence it is a random curve. Or maybe it holds when d goes to infinity? The numerical results are specific with k = 0.001d, which makes it hard to see if the Gaussian-k algorithm would still work using different k/d ratio. As shown in Figure 2, some of the histograms of u^1_t are quite sparse (these plots are hard to read for different iterations, maybe use cdf instead and perform statistical test to check how close to Gaussian distributions), therefore in some of these cases the Gaussian approximation may be poor. It is worth further investigation of the robustness of this algorithm as a replacement of the top-k algorithm.