Publications of Torsten Hoefler

Dan Alistarh, Torsten Hoefler, Mikael Johansson, Sarit Khirirat, Nikola Konstantinov, Cedric Renggli:

The Convergence of Sparsified Gradient Methods

(In Advances in Neural Information Processing Systems 31, presented in Montreal, Canada, Curran Associates, Inc., Dec. 2018)

Abstract

Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, largebatch methods, and gradient sparsification, have been proposed. To date, gradient sparsification methods–where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally–are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to three orders of magnitude, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.

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BibTeX

@incollection{top-k,
  author={Dan Alistarh and Torsten Hoefler and Mikael Johansson and Sarit Khirirat and Nikola Konstantinov and Cedric Renggli},
  title={{The Convergence of Sparsified Gradient Methods}},
  year={2018},
  month={Dec.},
  booktitle={Advances in Neural Information Processing Systems 31},
  location={Montreal, Canada},
  publisher={Curran Associates, Inc.},
  source={http://www.unixer.de/~htor/publications/},
}


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