Year: 2024
Type: preprint
Abstract: This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interface $Γ$ may be approximated by a connected series of hyperplanes with a prescribed accuracy $\varepsilon >0$, we show that a three-layer ReLU NN is sufficient to accurately approximate any piecewise constant function and establish its error bound. Moreover, if the discontinuity interface is convex, an analytical formula of the ReLU NN approximation with exact weights and biases is provided.
Source: arXiv (Cornell University)
Authors: Cai, Zhiqiang, Choi, Junpyo, Liu, Min
Institution: Purdue University West Lafayette
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4404260940