Neural Networks and Numerical Analysis

Description

The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences. The aim of the series is to be an active forum for the dissemination of up-to-date information in the form of authoritative works that will serve the applied mathematics community as the basis for further research. Editorial Board Rémi Abgrall, Universität Zürich, Switzerland José Antonio Carrillo de la Plata, University of Oxford, UK Jean-Michel Coron, Université Pierre et Marie Curie, Paris, France Athanassios S. Fokas, Cambridge University, UK Irene Fonseca, Carnegie Mellon University, Pittsburgh, USA This book uses numerical analysis as the main tool to investigate methods in machine learning and A.I. The e?ciency of neural network representation on for polynomial functions is studied in detail, together with an original description of the Latin hypercube method. In addition, unique features include the use of Tensor?ow for implementation on session and the application n to the construction of new optimized numerical schemes. Introduction Acknowledgement Contents 1 Objective functions, neural networks, and linear algebra 2 Approximation properties 3 A functional equation 4 Datasets 5 Stochastic gradient methods 6 Examples and research in the field Bibliography Index