Construction and approximation properties of exact neural network interpolation operators activated by entire functions

The construction and approximation properties of exact neural network interpolation are the important and challenging topics on approximation by neural networks. Most research on exact neural network interpolation has focused on establishing existence, with very few specifically constructed interpol...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of approximation theory Jg. 312; S. 106215
1. Verfasser: Yu, Dansheng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.12.2025
Schlagworte:
Approximation rate
Exact neural network interpolation
Modulus of continuity
Exact neural network interpolation
Modulus of continuity
Approximation rate
ISSN:0021-9045
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The construction and approximation properties of exact neural network interpolation are the important and challenging topics on approximation by neural networks. Most research on exact neural network interpolation has focused on establishing existence, with very few specifically constructed interpolation neural networks proposed. The main purpose of the present paper is to provide a method for directly constructing exact neural network interpolation operators, which has the advantages that all the components in the neural network operators are explicitly known, such as the coefficients, the weights and the thresholds. By employing some important methods in approximation theory, such as the equivalence between the K−functional and the modulus of continuity of the function, Berens–Lorentz Lemma, and two useful estimates of the derivatives of the operators, we establish both the direct and the converse results of approximation by the new interpolation operators, and thus obtain an equivalence characterization theorem. We also introduce a type of neural network interpolation operators with four layers and a type of max-product neural network operators, rigorously analyzing their approximation properties.
ISSN:0021-9045
DOI:10.1016/j.jat.2025.106215