Neural Networks and Numerical Analysis

Bruno Després

Published by De Gruyter 2022

Neural Networks and Numerical Analysis

Bruno Després

Volume 6 in the series De Gruyter Series in Applied and Numerical Mathematics

https://doi.org/10.1515/9783110783186

Overview
Contents

About this book

This book uses numerical analysis as the main tool to investigate methods in machine learning and neural networks. The efficiency of neural network representations for general functions and for polynomial functions is studied in detail, together with an original description of the Latin hypercube method and of the ADAM algorithm for training. Furthermore, unique features include the use of Tensorflow for implementation session, and the description of on going research about the construction of new optimized numerical schemes.

This timely volume uses numerical analysis as the main tool to study methods in machine learning and artificial intelligence. It explains mathematical notions, such as approximation and optimization, which are the roots of neural networks.

Author / Editor information

Bruno Després, Sorbonne University, France.

Topics

Frontmatter Publicly Available Download PDF	I
Introduction Publicly Available Download PDF	V
Acknowledgement Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XIII
1 Objective functions, neural networks, and linear algebra Requires Authentication Unlicensed Licensed Download PDF	1
2 Approximation properties Requires Authentication Unlicensed Licensed Download PDF	27
3 A functional equation Requires Authentication Unlicensed Licensed Download PDF	65
4 Datasets Requires Authentication Unlicensed Licensed Download PDF	81
5 Stochastic gradient methods Requires Authentication Unlicensed Licensed Download PDF	107
6 Examples and research in the field Requires Authentication Unlicensed Licensed Download PDF	131
Bibliography Requires Authentication Unlicensed Licensed Download PDF	149
Index Requires Authentication Unlicensed Licensed Download PDF	155

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Institutional Libraries, researchers and graduates students working in neural networks, A.I. and machine learning.
Pages
- Front matter: 16
- Main content: 158
Illustrations
- Illustrations: 18
- Coloured Illustrations: 11
Keywords: neural networks; machine learning; artificial initelligence; Tensorﬂow; numerical schemes; partial differential equations.

eBook

Published: August 22, 2022
ISBN: 9783110783186

Hardcover

Published: August 22, 2022
ISBN: 9783110783124