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arXiv · 2407.16293

A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to the sparsification of auto-encoders neural networks

Michel Barlaud·Guillaume Perez·Jean-Paul Marmorat
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Abstract

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.

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Michel Barlaud, Guillaume Perez, Jean-Paul Marmorat. 2024-07-23. A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to the sparsification of auto-encoders neural networks. https://arxiv.org/abs/2407.16293

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