带参数$\{0,\pm \frac{1}{2}, \pm 1, 2\}$的深度神经网络的函数逼近
Function approximation by deep neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$
摘要：
本文证明了$C_β$ -光滑函数可以通过具有ReLU激活函数和参数$\{0,\pm \frac{1}{2}, \pm 1, 2\}$的深度神经网络来近似。因此，所考虑的网络的$l_0$和$l_1$参数范数是等价的。所构造的网络的深度、宽度和有效参数的数量具有与$[-1,1]$中的参数网络相同的对近似误差的依赖性，直到对数因子。特别是，这意味着非参数回归估计与构造的网络达到相同的收敛速度与稀疏网络的参数在$[-1,1]$。
英文摘要：
In this paper it is shown that $C_β$-smooth functions can be approximated by deep neural networks with ReLU activation function and with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The $l_0$ and $l_1$ parameter norms of considered networks are thus equivalent. The depth, width and the number of active parameters of the constructed networks have, up to a logarithmic factor, the same dependence on the approximation error as the networks with parameters in $[-1,1]$. In particular, this means that the nonparametric regression estimation with the constructed networks attains the same convergence rate as with sparse networks with parameters in $[-1,1]$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
