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# Adaptive Gradient Quantization for Data-Parallel SGD

NIPS 2020, (2020)

EI

Abstract

Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training. We empirically observe that the statistics of gradients of deep models change during the training. Motivated by this observation, we introduce two adaptive quantization schemes, ALQ and...More

Introduction

- Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training.
- The authors empirically observe that the statistics of gradients of deep models change during the training
- Motivated by this observation, the authors introduce two adaptive quantization schemes, ALQ and AMQ.
- The authors introduce two adaptive quantization schemes, ALQ and AMQ
- In both schemes, processors update their compression schemes in parallel by efficiently computing sufficient statistics of a parametric distribution.
- 1e4 want distributed optimization methods that match the per- Figure 1: Changes in the average variance of formance of SGD on a single hypothetical super machine, normalized gradient coordinates in a ResNetwhile paying a negligible communication cost

Highlights

- Many communication-efficient variants of Stochastic gradient descent (SGD) use gradient quantization schemes
- We propose two adaptive methods for quantizing the gradients in data-parallel SGD
- We improve the validation accuracy by almost 2% on CIFAR-10 and 1% on ImageNet in challenging low-cost communication setups
- We provide theoretical guarantees for adaptively quantized SGD (AQSGD) algorithm, obtain variance and code-length bounds, and convergence guarantees for convex, nonconvex, and momentum-based variants of AQSGD
- To reduce communication costs of data-parallel SGD, we introduce two adaptively quantized methods, Adaptive Level Quantization (ALQ) and Adaptive Multiplier Quantization (AMQ), to learn and adapt gradient quantization method on the fly
- We demonstrate the superiority of ALQ and AMQ over nonadaptive methods empirically on deep models and large datasets

Methods

- ResNet-110 on CIFAR-10

ResNet-32 on CIFAR-10

ResNet-18 on ImageNet Bucket Size SuperSGD

NUQSGD [21, 22] QSGDinf [20] TRN [15]

ALQ ALQ-N AMQ AMQ-N Loss Loss Loss

SuperSGD ALQ AMQ Qinf TRN

Training Iteration (a) ResNet-32 on CIFAR-10

(b) ResNet-110 on CIFAR-10. - ResNet-18 on ImageNet Bucket Size SuperSGD.
- For bucket size 100 and 3 bits, NUQSGD performs nearly as good as adaptive methods but quickly loses accuracy as the bucket size grows or shrinks.
- QSGDinf stays competitive for a wider range of bucket sizes but still loses accuracy faster than other methods.
- This shows the impact of bucketing as an understudied trick in evaluating quantization methods

Results

- The authors improve the validation accuracy by almost 2% on CIFAR-10 and 1% on ImageNet in challenging low-cost communication setups.
- ALQ, achieves the best overall performance on ImageNet and the gap on CIFAR-10 with ALQ-N is less than 0.3%

Conclusion

- To reduce communication costs of data-parallel SGD, the authors introduce two adaptively quantized methods, ALQ and AMQ, to learn and adapt gradient quantization method on the fly.
- In addition to quantization method, in both methods, processors learn and adapt their coding methods in parallel by efficiently computing sufficient statistics of a parametric distribution.
- The authors establish a number of convergence guarantees for the adaptive methods.

- Table1: Validation accuracy on CIFAR-10 and ImageNet using 3 bits (except for SuperSGD and TRN) with 4 GPUs
- Table2: Validation accuracy of ResNet32 on CIFAR-10 using 3 quantization bits (except for SuperSGD and TRN) and bucket size 16384
- Table3: Training Hyper-parameters for CIFAR-10 and ImageNet
- Table4: Validation Accuracy on Full ImageNet Run
- Table5: Training ResNet50 on ImageNet with min-batch size 512. Time per step for training with 32bits full-precision is 1.2s and with 16 bits full-precision is 0.61s
- Table6: Training ResNet18 on ImageNet with min-batch size 512. Time per step for training with 32bits full-precision is 0.57s and with 16 bits full-precision is 0.28s
- Table7: Additional overhead of proposed methods for training ResNet18 on ImageNet (Table 6). We also show the cost of performing 3 updates relative to the total cost of training for 60 epochs. Full-precision training for 60 epochs with 32 bits takes 95 hours while with 16 bits takes 46 hours

Related work

- Adaptive quantization has been used for speech communication and storage [18]. In machine learning, several biased and unbiased schemes have been proposed to compress networks and gradients. Recently, lattice-based quantization has been studied for distributed mean estimation and variance reduction [19]. In this work, we focus on unbiased and coordinate-wise schemes to compress gradients.

Alistarh et al [20] proposed Quantized SGD (QSGD) focusing on the uniform quantization of stochastic gradients normalized to have unit Euclidean norm. Their experiments illustrate a similar quantization method, where gradients are normalized to have unit L∞ norm, achieves better performance. We refer to this method as QSGDinf or Qinf in short. Wen et al [15] proposed TernGrad, which can be viewed as a special case of QSGDinf with three quantization levels.

Funding

- FF was supported by OGS Scholarship
- DA and IM were supported the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 805223 ScaleML)
- DMR was supported by an NSERC Discovery Grant
- ARK was supported by NSERC Postdoctoral Fellowship
- Resources used in preparing this research were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute.5

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