Neural Networks and Numerical Analysis
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Bruno Després
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
Topics
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Frontmatter
I -
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Introduction
V -
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Acknowledgement
XI -
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Contents
XIII -
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1 Objective functions, neural networks, and linear algebra
1 -
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2 Approximation properties
27 -
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3 A functional equation
65 -
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4 Datasets
81 -
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5 Stochastic gradient methods
107 -
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6 Examples and research in the field
131 -
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Bibliography
149 -
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Index
155
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