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Large-scale distributed linear algebra with tensor processing units.

Adam G M Lewis1,2, Jackson Beall1,2, Martin Ganahl1,2

  • 1Simulation & Optimization Team, Sandbox AQ, Palo Alto, CA 94301.

Proceedings of the National Academy of Sciences of the United States of America
|August 8, 2022
PubMed
Summary
This summary is machine-generated.

Google Tensor Processing Units (TPUs), designed for machine learning, are repurposed as powerful supercomputers for dense linear algebra. These TPUs demonstrate significant scaling and performance for matrix multiplication and other linear algebra tasks.

Keywords:
ASICsTPUsdistributed computinglinear algebrascientific computation

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Area of Science:

  • High-performance computing
  • Applied mathematics
  • Computer architecture

Background:

  • Tensor Processing Units (TPUs) are specialized hardware accelerators developed for machine learning.
  • Dense linear algebra operations are fundamental to many scientific and engineering disciplines.
  • Repurposing existing hardware can offer cost-effective solutions for specialized computational needs.

Purpose of the Study:

  • To investigate the feasibility of using Google TPUs for large-scale dense linear algebra computations.
  • To evaluate the performance and scalability of TPUs in this new application domain.
  • To demonstrate the effectiveness of curated algorithms on TPU architecture for linear algebra tasks.

Main Methods:

  • Repurposing Google TPUs, originally designed for machine learning, into supercomputers for dense linear algebra.
  • Utilizing TPUs' fast intercore interconnects (ICIs), 2D network topology, and high-bandwidth memory (HBM).
  • Developing and applying distributed matrix multiplication algorithms optimized for TPU architecture.

Main Results:

  • TPUs achieve computationally bound regimes where matrix-multiply units (MXUs) dominate runtime, enabling impressive scaling and performance.
  • A 2,048-core TPU pod can perform matrix multiplication of size [Formula: see text] in approximately 2 minutes using float32 precision.
  • Curated algorithms allow other dense linear algebra tasks, including QR decomposition, linear system resolution, and matrix function computation (e.g., matrix polar factorization), to scale effectively.

Conclusions:

  • Google TPUs can be successfully repurposed as high-performance supercomputers for dense linear algebra.
  • The architecture of TPUs, particularly their interconnects and memory, is well-suited for computationally intensive linear algebra operations.
  • This repurposing opens new avenues for accelerating scientific computations using machine learning hardware.