Approximation properties of random shallow neural networks

Olov Per Schavemaker

doi:10.33540/3361

Approximation properties of random shallow neural networks

Olov Per Schavemaker

Research output: Thesis › Doctoral thesis 1 (Research UU / Graduation UU)

Abstract

We investigated how well certain classes of functions, such as Lipschitz continuous functions and Barron functions, can be approximated by partly random shallow neural networks. We also looked into related questions: function approximation with multivariate ridge functions (a generalization of shallow neural networks) and the probability a partly random hyperplane (a random neural network layer without activation function) will separate two disjoint Euclidean balls.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	Utrecht University
Supervisors/Advisors	Dirksen, Sjoerd, Supervisor Salanevich, Palina, Co-supervisor
Award date	31 Mar 2026
Publisher	Utrecht University
DOIs	https://doi.org/10.33540/3361
Publication status	Published - 31 Mar 2026

Keywords

artificial neural networks
approximation
probability
harmonic analysis

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title = "Approximation properties of random shallow neural networks",

abstract = "We investigated how well certain classes of functions, such as Lipschitz continuous functions and Barron functions, can be approximated by partly random shallow neural networks. We also looked into related questions: function approximation with multivariate ridge functions (a generalization of shallow neural networks) and the probability a partly random hyperplane (a random neural network layer without activation function) will separate two disjoint Euclidean balls.",

keywords = "-, artificial neural networks, approximation, probability, harmonic analysis",

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year = "2026",

month = mar,

day = "31",

doi = "10.33540/3361",

language = "English",

publisher = "Utrecht University",

type = "Doctoral thesis 1 (Research UU / Graduation UU)",

school = "Universiteit Utrecht",

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AU - Schavemaker, Olov Per

PY - 2026/3/31

Y1 - 2026/3/31

N2 - We investigated how well certain classes of functions, such as Lipschitz continuous functions and Barron functions, can be approximated by partly random shallow neural networks. We also looked into related questions: function approximation with multivariate ridge functions (a generalization of shallow neural networks) and the probability a partly random hyperplane (a random neural network layer without activation function) will separate two disjoint Euclidean balls.

AB - We investigated how well certain classes of functions, such as Lipschitz continuous functions and Barron functions, can be approximated by partly random shallow neural networks. We also looked into related questions: function approximation with multivariate ridge functions (a generalization of shallow neural networks) and the probability a partly random hyperplane (a random neural network layer without activation function) will separate two disjoint Euclidean balls.

KW - -

KW - artificial neural networks

KW - approximation

KW - probability

KW - harmonic analysis

U2 - 10.33540/3361

DO - 10.33540/3361

M3 - Doctoral thesis 1 (Research UU / Graduation UU)

PB - Utrecht University

ER -

Approximation properties of random shallow neural networks

Abstract

Keywords

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