Large-scale distributed linear algebra with tensor processing units.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 35939669.
- Also identified by DOI 10.1073/pnas.2122762119 and PMC identifier 9388123.
- Licence recorded as CC BY-NC-ND.
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Abstract
We have repurposed Google tensor processing units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast intercore interconnects (ICIs), physically two-dimensional network topology, and high-bandwidth memory (HBM) permit distributed matrix multiplication algorithms to rapidly become computationally bound. In this regime, the matrix-multiply units (MXUs) dominate the runtime, yielding impressive scaling, performance, and raw size: Operating in float32 precision, a full 2,048-core pod of third-generation TPUs can multiply two matrices with linear size [Formula: see text] in about 2 min. Via curated algorithms emphasizing large, single-core matrix multiplications, other tasks in dense linear algebra can similarly scale. As examples, we present 1) QR decomposition; 2) resolution of linear systems; and 3) the computation of matrix functions by polynomial iteration, demonstrated by the matrix polar factorization.