Minimum width for universal approximation using ReLU networks on compact domain

arXiv:2309.10402v2 Announce Type: replace
Abstract: It has been shown that deep neural networks of a large enough width are universal approximators but they are not if the width is too small. There were several attempts to characterize the minimum width $w_{\min}$ enabling the universal approximation property; however, only a few of them found the exact values. In this work, we show that the minimum width for $L^p$ approximation of $L^p$ functions from $[0,1]^{d_x}$ to $\mathbb R^{d_y}$ is exactly $\max\{d_x,d_y,2\}$ if …

abstract approximation arxiv cs.lg domain enabling networks neural networks property relu small stat.ml type universal