Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

arXiv:2607.04597v1 Announce Type: cross Abstract: In this paper, we study the universal approximation property of residual neural networks, and obtain some new results. For input and output dimensions $d_x$ and $d_y$, and LeakyReLU, ReLU, ReLU-like activation functions, the upper and lower bounds of the block width are established. To achieve $L^p$ approximation $(1\leq p