Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
In this paper, we study the universal approximation property of residual neural networks. For input and output dimensions $d_x$ and $d_y$, and LeakyReLU, ReLU, ReLU-like activation functions, the upper and lower bounds of the minimum block width are established. To achieve $L^p$ approximation $(1\leq p <+\infty)$ on any compact set, we show that the exact minimum block width is $\max\{d_x,d_y\}$ when each residual branch has inner width 1. Furthermore, we show that residual neural networks with block width $\min\{d_x+d_y, \max\{2d_x+1,d_y\}\}$ can achieve uniform approximation on any compact set under the constraint that each residual branch has inner width 1. Besides, for any activation ...
| Authors | Qi Zhou, Xuan Zhou, Xiao-Song Yang |
|---|---|
| Primary category | cs.LG |
| Published | 6 July 2026 |
| Last updated at source | 10 August 2026 |
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