no code implementations • 23 Mar 2022 • Zhihuai Chen, Siyao Guo, Qian Li, Chengyu Lin, Xiaoming Sun
We show how to distinguish circuits with $\log k$ negations (a. k. a $k$-monotone functions) from uniformly random functions in $\exp\left(\tilde{O}\left(n^{1/3}k^{2/3}\right)\right)$ time using random samples.
no code implementations • ICML 2018 • Alexandr Andoni, Chengyu Lin, Ying Sheng, Peilin Zhong, Ruiqi Zhong
An Orlicz norm is parameterized by a non-negative convex function $G:\mathbb{R}_+\rightarrow\mathbb{R}_+$ with $G(0)=0$: the Orlicz norm of a vector $x\in\mathbb{R}^n$ is defined as $ \|x\|_G=\inf\left\{\alpha>0\large\mid\sum_{i=1}^n G(|x_i|/\alpha)\leq 1\right\}.