Date of Award

6-2019

Document Type

Open Access

Degree Name

Bachelor of Science

Department

Mathematics

First Advisor

Professor George Todd

Keywords

real analysis, artificial neural network, universal approximation theorem, artificial intelligence

Abstract

An artificial neural network is a biologically-inspired system that can be trained to perform computations. Recently, techniques from machine learning have trained neural networks to perform a variety of tasks. It can be shown that any continuous function can be approximated by an artificial neural network with arbitrary precision. This is known as the universal approximation theorem. In this thesis, we will introduce neural networks and one of the first versions of this theorem, due to Cybenko. He modeled artificial neural networks using sigmoidal functions and used tools from measure theory and functional analysis.

Comments

Thanks for the support of my advisors and the math department to give me such a great research opportunity for this written thesis.

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