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Swing: Short-cutting Rings for Higher Bandwidth Allreduce

Daniele De Sensi, Tommaso Bonato, David Saam, Torsten Hoefler

TL;DR

Swing, a new algorithm that keeps a low distance between communicating nodes by swinging between torus directions, is introduced, which outperforms by up to 3x existing allreduce algorithms for vectors ranging from 32B to 128MiB, on different types of torus and torus-like topologies, regardless of their shape and size.

Abstract

The allreduce collective operation accounts for a significant fraction of the runtime of workloads running on distributed systems. One factor determining its performance is the distance between communicating nodes, especially on networks like torus, where a higher distance implies multiple messages being forwarded on the same link, thus reducing the allreduce bandwidth. Torus networks are widely used on systems optimized for machine learning workloads (e.g., Google TPUs and Amazon Trainium devices), as well as on some of the Top500 supercomputers. To improve allreduce performance on torus networks we introduce Swing, a new algorithm that keeps a low distance between communicating nodes by swinging between torus directions. Our analysis and experimental evaluation show that Swing outperforms by up to 3x existing allreduce algorithms for vectors ranging from 32B to 128MiB, on different types of torus and torus-like topologies, regardless of their shape and size.

Swing: Short-cutting Rings for Higher Bandwidth Allreduce

TL;DR

Swing, a new algorithm that keeps a low distance between communicating nodes by swinging between torus directions, is introduced, which outperforms by up to 3x existing allreduce algorithms for vectors ranging from 32B to 128MiB, on different types of torus and torus-like topologies, regardless of their shape and size.

Abstract

The allreduce collective operation accounts for a significant fraction of the runtime of workloads running on distributed systems. One factor determining its performance is the distance between communicating nodes, especially on networks like torus, where a higher distance implies multiple messages being forwarded on the same link, thus reducing the allreduce bandwidth. Torus networks are widely used on systems optimized for machine learning workloads (e.g., Google TPUs and Amazon Trainium devices), as well as on some of the Top500 supercomputers. To improve allreduce performance on torus networks we introduce Swing, a new algorithm that keeps a low distance between communicating nodes by swinging between torus directions. Our analysis and experimental evaluation show that Swing outperforms by up to 3x existing allreduce algorithms for vectors ranging from 32B to 128MiB, on different types of torus and torus-like topologies, regardless of their shape and size.
Paper Structure (41 sections, 5 theorems, 12 equations, 15 figures, 2 tables)

This paper contains 41 sections, 5 theorems, 12 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction and Motivation
  2. Background
  3. Targeted Collectives
  4. Notation and Model
  5. State-of-the Art Algorithms
  6. Hamiltonian Rings
  7. Latency-Optimal Recursive Doubling
  8. Non-power-of-two
  9. Bandwidth-Optimal Recursive Doubling
  10. Non-power-of-$2$
  11. Bucket Algorithm
  12. Other Approaches
  13. Topology-Specific Algorithms
  14. Automatic Generation of Collective Algorithms
  15. Topology Reconfiguration and In-Network Compute
  16. ...and 26 more sections

Key Result

Lemma A.1

$\rho(s)$ and $\delta(s)$ are odd $\forall s \in \mathbb{N}$.

Figures (15)

  • Figure 1: First three steps of the recursive doubling and Swing allreduce algorithms on a 1D torus with $16$ nodes.
  • Figure 2: Example of recursive doubling on a $4x4$ torus. Wrap-around links are not shown.
  • Figure 3: First 2 step of the Swing algorithm on a 1D torus with 7 nodes.
  • Figure 4: First step of the Swing algorithm on a 4x4 torus.
  • Figure 5: Multiport Swing collective on a 2x4 torus.
  • ...and 10 more figures

Theorems & Definitions (10)

  • Lemma A.1
  • proof
  • Lemma A.2
  • proof
  • Lemma A.3
  • proof
  • Lemma A.4
  • proof
  • Theorem A.5
  • proof