A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915970412445696 |
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| author | Song, Yue |
| author_facet | Song, Yue |
| contents | EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim${<}32$). This short paper targets the limitation and proposes a batch-efficient Divide-and-Conquer based ED algorithm for larger matrices. The numerical test shows that for a mini-batch of matrices whose dimensions are smaller than $64$, our method can be much faster than the Pytorch SVD function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition Song, Yue Machine Learning Numerical Analysis EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim${<}32$). This short paper targets the limitation and proposes a batch-efficient Divide-and-Conquer based ED algorithm for larger matrices. The numerical test shows that for a mini-batch of matrices whose dimensions are smaller than $64$, our method can be much faster than the Pytorch SVD function. |
| title | A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2604.27325 |