Fast Kronecker Matrix-Matrix Multiplication on GPUs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929258162552832 |
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| author | Jangda, Abhinav Yadav, Mohit |
| author_facet | Jangda, Abhinav Yadav, Mohit |
| contents | Kronecker Matrix-Matrix Multiplication (Kron-Matmul) is the multiplication of a matrix with the Kronecker Product of several smaller matrices. Kron-Matmul is a core operation for many scientific and machine learning computations. State-of-the-art Kron-Matmul implementations utilize existing tensor algebra operations, such as matrix multiplication, transpose, and tensor matrix multiplication. However, this design choice prevents several Kron-Matmul specific optimizations, thus, leaving significant performance on the table. To address this issue, we present FastKron, an efficient technique for Kron-Matmul on single and multiple GPUs. FastKron is independent of linear algebra operations enabling several new optimizations for Kron-Matmul. Thus, it performs up to 40.7x and 7.85x faster than existing implementations on 1 and 16 GPUs respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Kronecker Matrix-Matrix Multiplication on GPUs Jangda, Abhinav Yadav, Mohit Distributed, Parallel, and Cluster Computing Kronecker Matrix-Matrix Multiplication (Kron-Matmul) is the multiplication of a matrix with the Kronecker Product of several smaller matrices. Kron-Matmul is a core operation for many scientific and machine learning computations. State-of-the-art Kron-Matmul implementations utilize existing tensor algebra operations, such as matrix multiplication, transpose, and tensor matrix multiplication. However, this design choice prevents several Kron-Matmul specific optimizations, thus, leaving significant performance on the table. To address this issue, we present FastKron, an efficient technique for Kron-Matmul on single and multiple GPUs. FastKron is independent of linear algebra operations enabling several new optimizations for Kron-Matmul. Thus, it performs up to 40.7x and 7.85x faster than existing implementations on 1 and 16 GPUs respectively. |
| title | Fast Kronecker Matrix-Matrix Multiplication on GPUs |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2401.10187 |