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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.16293 |
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| _version_ | 1866915180880855040 |
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| author | Barlaud, Michel Perez, Guillaume Marmorat, Jean-Paul |
| author_facet | Barlaud, Michel Perez, Guillaume Marmorat, Jean-Paul |
| contents | The $\ell_{1,\infty}$ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, $\mathcal{O}\big(n m \log(n m)\big)$ for a matrix $n\times m$.\\ In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the $\ell_{1,\infty}$ norm is only $\mathcal{O}\big(n m \big)$ for a matrix $n\times m$. Moreover, we provide a new $\ell_{1,\infty}$ identity with mathematical proof and experimental validation. Experiments show that our bi-level $\ell_{1,\infty}$ projection is $2.5$ times faster than the actual fastest algorithm and provides the best sparsity while keeping the same accuracy in classification applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to the sparsification of auto-encoders neural networks Barlaud, Michel Perez, Guillaume Marmorat, Jean-Paul Machine Learning The $\ell_{1,\infty}$ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, $\mathcal{O}\big(n m \log(n m)\big)$ for a matrix $n\times m$.\\ In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the $\ell_{1,\infty}$ norm is only $\mathcal{O}\big(n m \big)$ for a matrix $n\times m$. Moreover, we provide a new $\ell_{1,\infty}$ identity with mathematical proof and experimental validation. Experiments show that our bi-level $\ell_{1,\infty}$ projection is $2.5$ times faster than the actual fastest algorithm and provides the best sparsity while keeping the same accuracy in classification applications. |
| title | A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to the sparsification of auto-encoders neural networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.16293 |