Sharp lower bounds on interpolation by deep ReLU neural networks at irregularly spaced data
Year: 2025
Type: article
Abstract: We study the interpolation power of deep ReLU neural networks. Specifically, we consider the question of how efficiently, in terms of the number of parameters, deep ReLU networks can interpolate values at N datapoints in the unit ball which are separated by a distance δ . We show that Ω ( N ) parameters are required in the regime where δ is exponentially small in N , which gives the sharp result in this regime since O ( N ) parameters are always sufficient. This also shows that the bit-extraction technique used to prove lower bounds on the VC dimension cannot be applied to irregularly spaced datapoints. Finally, as an application we give a lower bound on the approximation rates that deep ReLU neural networks can achieve for Sobolev spaces at the embedding endpoint.
Source: Journal of Approximation Theory
Author: Jonathan W. Siegel
Institution: Texas A&M University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,910
Awards: Comparative Study of Finite Element and Neural Network Discretizations for Partial Differential Equations, G3587679958, G5121974832, Comparative Study of Finite Element and Neural Network Discretizations for Partial Differential Equations, G6706517093, G8876996369, CIF: Small: Interpretable Machine Learning based on Deep Neural Networks: A Source Coding Perspective
OpenAlex ID: W4415215933