Neural Networks and Numerical Analysis

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.

Table of Contents

1 Objective functio ns, neural networks, and linear algebra

2 Approximation properties

3 A functio nal equation

4 Datasets

5 Stochastic g radient methods

6 Examples and research in the field