A new Linear Time Bi-level $\ell_{1,\infty}$ projection ; Application to the sparsification of auto-encoders neural networks
This work addresses a computational bottleneck in sparsifying auto-encoders for neural networks, offering an incremental improvement in efficiency for machine learning applications.
The paper tackles the computational inefficiency of the $\ell_{1,\infty}$ norm projection by proposing a new bi-level method that reduces time complexity from $\mathcal{O}(n m \log(n m))$ to $\mathcal{O}(n m)$, achieving a 2.5 times speedup and maintaining accuracy with improved sparsity in classification tasks.
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.