Large-scale distributed linear algebra with tensor processing units

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 N = 2(20) = 1,048,576 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.

Automated summary

Researchers have repurposed Google's TPUs to create large-scale dense linear algebra supercomputers, which can rapidly compute large matrices in less than two minutes using distributed matrix multiplication algorithms.