Multi-level projection with exponential parallel speedup; Application to sparse auto-encoders neural networks

arXiv:2405.02086v1 Announce Type: new
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 in $\mathbb{R}^{n\times m}$. 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 in $\mathbb{R}^{n\times m}$, and $\mathcal{O}\big(n + m \big)$ with full parallel power. We generalize our method to tensors …

abstract algorithm application arxiv auto big complexity cs.lg matrix networks neural networks norm paper projection show type