Error Analysis of Matrix Multiplication Emulation Using Ozaki-II Scheme
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908807689404416 |
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| author | Uchino, Yuki Ozaki, Katsuhisa Imamura, Toshiyuki |
| author_facet | Uchino, Yuki Ozaki, Katsuhisa Imamura, Toshiyuki |
| contents | The Ozaki-II scheme is an emulation method that leverages the Chinese Remainder Theorem to compute high-precision matrix multiplication via a sequence of low-precision matrix multiplications. In this scheme, the attainable numerical accuracy improves as the number of low-precision matrix multiplications increases. Previous numerical studies have shown that single- and double-precision matrix multiplication using the Ozaki-II scheme achieves higher throughput than that of standard BLAS routines on modern AI hardware equipped with fast INT8 matrix multiply-accumulate units with INT8 inputs and INT32 accumulation. However, the accuracy of the Ozaki-II scheme can degrade when the exponent distribution of the input matrices is wide, in which case a large number of low-precision matrix multiplications is required to obtain high-precision results. In this paper, we present a rigorous deterministic error analysis of the Ozaki-II scheme. The proposed analysis not only clarifies the accuracy behavior of the method but also enables the estimation of the number of low-precision matrix multiplications required to achieve a desired level of numerical accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error Analysis of Matrix Multiplication Emulation Using Ozaki-II Scheme Uchino, Yuki Ozaki, Katsuhisa Imamura, Toshiyuki Numerical Analysis Distributed, Parallel, and Cluster Computing The Ozaki-II scheme is an emulation method that leverages the Chinese Remainder Theorem to compute high-precision matrix multiplication via a sequence of low-precision matrix multiplications. In this scheme, the attainable numerical accuracy improves as the number of low-precision matrix multiplications increases. Previous numerical studies have shown that single- and double-precision matrix multiplication using the Ozaki-II scheme achieves higher throughput than that of standard BLAS routines on modern AI hardware equipped with fast INT8 matrix multiply-accumulate units with INT8 inputs and INT32 accumulation. However, the accuracy of the Ozaki-II scheme can degrade when the exponent distribution of the input matrices is wide, in which case a large number of low-precision matrix multiplications is required to obtain high-precision results. In this paper, we present a rigorous deterministic error analysis of the Ozaki-II scheme. The proposed analysis not only clarifies the accuracy behavior of the method but also enables the estimation of the number of low-precision matrix multiplications required to achieve a desired level of numerical accuracy. |
| title | Error Analysis of Matrix Multiplication Emulation Using Ozaki-II Scheme |
| topic | Numerical Analysis Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2602.02549 |