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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

Mixed precision randomized low-rank approximation with GPU tensor cores

Marc Baboulin
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Oguz Kaya
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Theo Mary
Matthieu Robeyns
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  • PersonId : 1367696

Résumé

Randomized projection methods have been shown to be very efficient at computing low-rank approximations (LRA) of large matri- ces. In this work, we investigate the design and development of such methods capable of exploiting recent mixed precision accelerators like GPUs equipped with tensor core units. We combine three new ideas to exploit mixed precision arithmetic in randomized LRA. The first is to perform the matrix multiplication with mixed precision fp16/fp32 ten- sor cores. The second is to use CholeskyQR orthonormalization, which is much faster on GPUs, while mitigating its numerical instability by using fp64 arithmetic. The third is to use a recently proposed iterative refine- ment method for LRA to improve the accuracy of the LRA by calling it twice. We implement the proposed approach on various GPU archi- tectures and analyze its performance and accuracy. We compare with a standard randomized LRA entirely in fp32 arithmetic, which achieves an average accuracy of order 10−4 . Our results show that our approach without refinement is up to 8× faster, with an average accuracy of order 10−2 , which may be acceptable for some applications. Otherwise, we show that using refinement significantly improves the accuracy to an average of order 10−5 , while remaining up to 2.2× faster than the standard fp32 randomized LRA. This work illustrates the convergence of approximate computing techniques by combining low-rank approximations, random- ization, mixed precision arithmetic, and GPU acceleration.
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Dates et versions

hal-04520893 , version 1 (25-03-2024)

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  • HAL Id : hal-04520893 , version 1

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Marc Baboulin, Simplice Donfack, Oguz Kaya, Theo Mary, Matthieu Robeyns. Mixed precision randomized low-rank approximation with GPU tensor cores. 2024. ⟨hal-04520893⟩
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