标题： ReLU网络中逼近光滑非线性函数的深度分离 显示英文标题

标题： Depth Separation in ReLU Networks for Approximating Smooth Non-Linear Functions

摘要： 我们提供了一个基于深度的分离结果，用于前馈ReLU神经网络，表明在$[0,1]^d$上的一类非线性、二阶可微函数，可以通过深度和宽度为$\mathcal{O}(\text{poly}(\log(1/\epsilon)))$的ReLU网络以精度$\epsilon$进行近似，但除非其宽度至少为$\Omega(1/\epsilon)$，否则无法通过常数深度的ReLU网络以类似的精度进行近似。 显示英文摘要

摘要： We provide a depth-based separation result for feed-forward ReLU neural networks, showing that a wide family of non-linear, twice-differentiable functions on $[0,1]^d$, which can be approximated to accuracy $\epsilon$ by ReLU networks of depth and width $\mathcal{O}(\text{poly}(\log(1/\epsilon)))$, cannot be approximated to similar accuracy by constant-depth ReLU networks, unless their width is at least $\Omega(1/\epsilon)$.