Distributed and heterogeneous tensor–vector contraction algorithms for high performance computing
The tensor–vector contraction (TVC) is the most memory-bound operation of its class and a core component of the higher-order power method (HOPM). This paper brings distributed-memory parallelization to a native TVC algorithm for dense tensors that overall remains oblivious to contraction mode, tenso...
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| Vydáno v: | Future generation computer systems Ročník 166; s. 107698 |
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01.05.2025
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| Abstract | The tensor–vector contraction (TVC) is the most memory-bound operation of its class and a core component of the higher-order power method (HOPM). This paper brings distributed-memory parallelization to a native TVC algorithm for dense tensors that overall remains oblivious to contraction mode, tensor splitting, and tensor order. Similarly, we propose a novel distributed HOPM, namely dHOPM3, that can save up to one order of magnitude of streamed memory and is about twice as costly in terms of data movement as a distributed TVC operation (dTVC) when using task-based parallelization. The numerical experiments carried out in this work on three different architectures featuring multicore and accelerators confirm that the performances of dTVC and dHOPM3 remain relatively close to the peak system memory bandwidth (50%–80%, depending on the architecture) and on par with STREAM benchmark figures. On strong scalability scenarios, our native multicore implementations of these two algorithms can achieve similar and sometimes even greater performance figures than those based upon state-of-the-art CUDA batched kernels. Finally, we demonstrate that both computation and communication can benefit from mixed precision arithmetic also in cases where the hardware does not support low precision data types natively.
•A novel distributed tensor–vector contraction algorithm is introduced.•Analytical formulae are derived for minimal data movement and best throughput.•A best-in-class higher order power method with task-based parallelization is given.•Our dTVC and dHOPM3 algorithms reach 50% to 80% of the theoretical peak bandwidth.•Our cached, mixed precision ad-hoc kernels speedup computation and communication. |
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| AbstractList | The tensor–vector contraction (TVC) is the most memory-bound operation of its class and a core component of the higher-order power method (HOPM). This paper brings distributed-memory parallelization to a native TVC algorithm for dense tensors that overall remains oblivious to contraction mode, tensor splitting, and tensor order. Similarly, we propose a novel distributed HOPM, namely dHOPM3, that can save up to one order of magnitude of streamed memory and is about twice as costly in terms of data movement as a distributed TVC operation (dTVC) when using task-based parallelization. The numerical experiments carried out in this work on three different architectures featuring multicore and accelerators confirm that the performances of dTVC and dHOPM3 remain relatively close to the peak system memory bandwidth (50%–80%, depending on the architecture) and on par with STREAM benchmark figures. On strong scalability scenarios, our native multicore implementations of these two algorithms can achieve similar and sometimes even greater performance figures than those based upon state-of-the-art CUDA batched kernels. Finally, we demonstrate that both computation and communication can benefit from mixed precision arithmetic also in cases where the hardware does not support low precision data types natively.
•A novel distributed tensor–vector contraction algorithm is introduced.•Analytical formulae are derived for minimal data movement and best throughput.•A best-in-class higher order power method with task-based parallelization is given.•Our dTVC and dHOPM3 algorithms reach 50% to 80% of the theoretical peak bandwidth.•Our cached, mixed precision ad-hoc kernels speedup computation and communication. |
| ArticleNumber | 107698 |
| Author | Beltran, Vicenç Martinez-Ferrer, Pedro J. Yzelman, Albert-Jan |
| Author_xml | – sequence: 1 givenname: Pedro J. orcidid: 0000-0002-6097-6676 surname: Martinez-Ferrer fullname: Martinez-Ferrer, Pedro J. email: pedro.martinez.ferrer@upc.edu organization: Departament d’Arquitectura de Computadors (DAC), Universitat Politècnica de Catalunya - BarcelonaTech (UPC), Campus Nord, Edif. D6, C. Jordi Girona 1-3, Barcelona, 08034, Cataluña, Spain – sequence: 2 givenname: Albert-Jan orcidid: 0000-0001-8842-3689 surname: Yzelman fullname: Yzelman, Albert-Jan email: albert-jan@yzelman.net organization: Computing Systems Laboratory, Huawei Technologies Switzerland AG, Thurgauerstrasse 80, Zürich, 8050, Dübendorf, Switzerland – sequence: 3 givenname: Vicenç orcidid: 0000-0002-3580-9630 surname: Beltran fullname: Beltran, Vicenç email: vbeltran@bsc.es organization: Barcelona Supercomputing Center (BSC), Pl. Eusebi Güell 1-3, Barcelona, 08034, Cataluña, Spain |
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| Cites_doi | 10.1016/j.jocs.2019.02.007 10.1109/99.660313 10.1002/cpe.1206 10.1137/07070111X 10.1016/j.jpdc.2014.06.002 10.1016/0167-8191(94)90033-7 10.1109/TPDS.2022.3153113 10.1007/BF02289464 10.1137/S0895479898346995 10.1145/2764454 10.1016/j.jpdc.2023.04.012 10.3389/fdata.2020.594302 |
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