Rethinking gradient sparsification as total error minimization

• URL: http://arxiv.org/abs/2108.00951v1
• Date: Mon, 2 Aug 2021 14:52:42 GMT
• Title: Rethinking gradient sparsification as total error minimization
• Authors: Atal Narayan Sahu (1), Aritra Dutta (1), Ahmed M. Abdelmoniem (1), Trambak Banerjee (2), Marco Canini (1), Panos Kalnis (1) ((1) KAUST, (2) University of Kansas)
• Abstract summary: Gradient compression is a widely-established remedy to tackle the communication bottleneck in distributed training training networks (DNNs) We argue that the benefits of gradient sparsification, especially for DNNs, are necessary -- one that moves from perit optimality to consider optimality for the entire training.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gradient compression is a widely-established remedy to tackle the communication bottleneck in distributed training of large deep neural networks (DNNs). Under the error-feedback framework, Top-$k$ sparsification, sometimes with $k$ as little as $0.1\%$ of the gradient size, enables training to the same model quality as the uncompressed case for a similar iteration count. From the optimization perspective, we find that Top-$k$ is the communication-optimal sparsifier given a per-iteration $k$ element budget. We argue that to further the benefits of gradient sparsification, especially for DNNs, a different perspective is necessary -- one that moves from per-iteration optimality to consider optimality for the entire training. We identify that the total error -- the sum of the compression errors for all iterations -- encapsulates sparsification throughout training. Then, we propose a communication complexity model that minimizes the total error under a communication budget for the entire training. We find that the hard-threshold sparsifier, a variant of the Top-$k$ sparsifier with $k$ determined by a constant hard-threshold, is the optimal sparsifier for this model. Motivated by this, we provide convex and non-convex convergence analyses for the hard-threshold sparsifier with error-feedback. Unlike with Top-$k$ sparsifier, we show that hard-threshold has the same asymptotic convergence and linear speedup property as SGD in the convex case and has no impact on the data-heterogeneity in the non-convex case. Our diverse experiments on various DNNs and a logistic regression model demonstrated that the hard-threshold sparsifier is more communication-efficient than Top-$k$.

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