---
_id: '6589'
abstract:
- lang: eng
  text: 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, large-batch
    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 \emph{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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan-Adrian
  full_name: Alistarh, Dan-Adrian
  id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
  last_name: Alistarh
  orcid: 0000-0003-3650-940X
- first_name: Torsten
  full_name: Hoefler, Torsten
  last_name: Hoefler
- first_name: Mikael
  full_name: Johansson, Mikael
  last_name: Johansson
- first_name: Nikola H
  full_name: Konstantinov, Nikola H
  id: 4B9D76E4-F248-11E8-B48F-1D18A9856A87
  last_name: Konstantinov
- first_name: Sarit
  full_name: Khirirat, Sarit
  last_name: Khirirat
- first_name: Cedric
  full_name: Renggli, Cedric
  last_name: Renggli
citation:
  ama: 'Alistarh D-A, Hoefler T, Johansson M, Konstantinov NH, Khirirat S, Renggli
    C. The convergence of sparsified gradient methods. In: <i>Advances in Neural Information
    Processing Systems 31</i>. Vol Volume 2018. Neural Information Processing Systems
    Foundation; 2018:5973-5983.'
  apa: 'Alistarh, D.-A., Hoefler, T., Johansson, M., Konstantinov, N. H., Khirirat,
    S., &#38; Renggli, C. (2018). The convergence of sparsified gradient methods.
    In <i>Advances in Neural Information Processing Systems 31</i> (Vol. Volume 2018,
    pp. 5973–5983). Montreal, Canada: Neural Information Processing Systems Foundation.'
  chicago: Alistarh, Dan-Adrian, Torsten Hoefler, Mikael Johansson, Nikola H Konstantinov,
    Sarit Khirirat, and Cedric Renggli. “The Convergence of Sparsified Gradient Methods.”
    In <i>Advances in Neural Information Processing Systems 31</i>, Volume 2018:5973–83.
    Neural Information Processing Systems Foundation, 2018.
  ieee: D.-A. Alistarh, T. Hoefler, M. Johansson, N. H. Konstantinov, S. Khirirat,
    and C. Renggli, “The convergence of sparsified gradient methods,” in <i>Advances
    in Neural Information Processing Systems 31</i>, Montreal, Canada, 2018, vol.
    Volume 2018, pp. 5973–5983.
  ista: 'Alistarh D-A, Hoefler T, Johansson M, Konstantinov NH, Khirirat S, Renggli
    C. 2018. The convergence of sparsified gradient methods. Advances in Neural Information
    Processing Systems 31. NeurIPS: Conference on Neural Information Processing Systems
    vol. Volume 2018, 5973–5983.'
  mla: Alistarh, Dan-Adrian, et al. “The Convergence of Sparsified Gradient Methods.”
    <i>Advances in Neural Information Processing Systems 31</i>, vol. Volume 2018,
    Neural Information Processing Systems Foundation, 2018, pp. 5973–83.
  short: D.-A. Alistarh, T. Hoefler, M. Johansson, N.H. Konstantinov, S. Khirirat,
    C. Renggli, in:, Advances in Neural Information Processing Systems 31, Neural
    Information Processing Systems Foundation, 2018, pp. 5973–5983.
conference:
  end_date: 2018-12-08
  location: Montreal, Canada
  name: 'NeurIPS: Conference on Neural Information Processing Systems'
  start_date: 2018-12-02
corr_author: '1'
date_created: 2019-06-27T09:32:55Z
date_published: 2018-12-01T00:00:00Z
date_updated: 2025-06-26T12:23:06Z
day: '01'
department:
- _id: DaAl
- _id: ChLa
ec_funded: 1
external_id:
  arxiv:
  - '1809.10505'
  isi:
  - '000461852000047'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1809.10505
month: '12'
oa: 1
oa_version: Preprint
page: 5973-5983
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: Advances in Neural Information Processing Systems 31
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
scopus_import: '1'
status: public
title: The convergence of sparsified gradient methods
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: Volume 2018
year: '2018'
...