Year: 2024
Type: preprint
Abstract: In this work, we consider the approximation of a large class of bounded functions, with minimal regularity assumptions, by ReLU neural networks. We show that the approximation error can be bounded from above by a quantity proportional to the uniform norm of the target function and inversely proportional to the product of network width and depth. We inherit this approximation error bound from Fourier features residual networks, a type of neural network that uses complex exponential activation functions. Our proof is constructive and proceeds by conducting a careful complexity analysis associated with the approximation of a Fourier features residual network by a ReLU network.
Source: arXiv (Cornell University)
Institutions: University of New Mexico, Sandia National Laboratories
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G11630931, G2214935549, G413247060, G4903105778
OpenAlex ID: W4396912949