A new Linear Time Bi-level $\ell_1,\infty$ projection ; Application to the sparsification of auto-encoders neural networks
<|reference_start|>A new Linear Time Bi-level $\ell_1,\infty$ projection ; Application to the sparsification of auto-encoders neural networks: 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.<|reference_end|>
@article{barlaud2024a,
    title={A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to
  the sparsification of auto-encoders neural networks},
    author={Michel Barlaud, Guillaume Perez and Jean-Paul Marmorat},
    journal={arXiv preprint arXiv:2407.16293},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16293},
    primaryClass={cs.LG}
}