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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.09814 |
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| _version_ | 1866913841074405376 |
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| author | Rybin, Dmitry Zhang, Yushun Luo, Zhi-Quan |
| author_facet | Rybin, Dmitry Zhang, Yushun Luo, Zhi-Quan |
| contents | We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $XX^{t}$ Can Be Faster Rybin, Dmitry Zhang, Yushun Luo, Zhi-Quan Data Structures and Algorithms Artificial Intelligence Machine Learning Symbolic Computation 68Q25, 68T20 F.2.1; I.1.2 We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization. |
| title | $XX^{t}$ Can Be Faster |
| topic | Data Structures and Algorithms Artificial Intelligence Machine Learning Symbolic Computation 68Q25, 68T20 F.2.1; I.1.2 |
| url | https://arxiv.org/abs/2505.09814 |