Multilayer Neural Networks

A Generalized Net Perspective

verfasst von: Maciej Krawczak

Verlag: Springer International Publishing

Buchreihe : Studies in Computational Intelligence

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The primary purpose of this book is to show that a multilayer neural network can be considered as a multistage system, and then that the learning of this class of neural networks can be treated as a special sort of the optimal control problem. In this way, the optimal control problem methodology, like dynamic programming, with modifications, can yield a new class of learning algorithms for multilayer neural networks.

Another purpose of this book is to show that the generalized net theory can be successfully used as a new description of multilayer neural networks. Several generalized net descriptions of neural networks functioning processes are considered, namely: the simulation process of networks, a system of neural networks and the learning algorithms developed in this book.

The generalized net approach to modelling of real systems may be used successfully for the description of a variety of technological and intellectual problems, it can be used not only for representing the parallel functioning of homogenous objects, but also for modelling non-homogenous systems, for example systems which consist of a different kind of subsystems.

The use of the generalized nets methodology shows a new way to describe functioning of discrete dynamic systems.

Inhaltsverzeichnis

Frontmatter

Introduction to Multilayer Neural Networks

Abstract

The notion of sequential computation is based on the von Neumann machine (von Neumann 1966) whose functioning can be displayed in a very simple, symbolic way (Fig. 1.1). The first part of the respective machinery, called memory, serves as a store of computer programmes with instructions, whereas the second part, called processor, in which an ordinary arithmetic rule of addition is performed within an operation system.

Maciej Krawczak

Basics of Generalized Nets

Abstract

The concept generalized nets was described by Krassimir Atanassov in 1982.

Since that time hundreds papers and several books have been published. In Review and bibliography on generalized nets theory and applications by Radeva, Krawczak and Choy (2002), one can find the list of 353 scientific works related to the generalized nets.

Maciej Krawczak

Simulation Process of Neural Networks

Abstract

Due to Cybenko’s theorem, described in Sect. 1.5, multilayer feedforward neural networks are universal approximators or universal classifiers. Approximation or classification done by neural networks is performed during the simulation process described in Sect. 1.2.

Maciej Krawczak

Learning from Examples

Abstract

The process of learning from examples (or supervised learning) of multilayer neural networks can be considered when a set {input _p, output _p } , p = 1,2,...,P , is available. The aim is to configure a neural network in such a way as to generate the definite output if the respective input feeds the network.

Maciej Krawczak

Learning as a Control Process

Abstract

The commonly used algorithm for the multilayer neural networks learning, the backpropagation algorithm described in the Chap. 4, is a gradient descent method for searching minimum of a performance index of learning. The performance index, being the measure of neural network learning quality, is a multimodal function. Application of this kind of algorithms causes frequent stopping at a local minimum. Various modifications of this algorithm still cannot avoid local minimal points. Until now, in practice, the only way of trying to find the near global optimum solution is to perform computation several times with different initial weight values and then to choose the best solution.

Maciej Krawczak

Parameterisation of Learning

Abstract

Learning of a neural network is meant to adjust connections between layers (connections between neurons) in order to minimize the performance index of learning. For this, the backpropagation algorithm with various modifications is commonly used. At the same time, the learning process of multilayer neural networks can be considered as a particular multistage optimal control problem, described in Chap. 4.

Maciej Krawczak

Adjoint Neural Networks

Abstract

In the very rich artificial neural networks literature little attention has been given to consideration of neural networks from the point of graph theory. Examination of neural networks as flow graphs gives very interesting and new properties of the neural networks learning process.

Maciej Krawczak

Summary

Abstract

In this book, the natural structure of multilayer neural networks was used in order to consider this class of neural networks from the systems point of view: the aggregated neurons lying within one layer constitute the stage of the system and the bordering stages exchange the information on their states. The outputs of the neurons, from the same layer, constitute the state vectors. Connection weights between the neurons of the same layer are arranged in vectors and are treated as controls. In this way, we developed the interpretation of the multilayer neural networks as the multistage control systems.

Maciej Krawczak

Backmatter

Titel: Multilayer Neural Networks
verfasst von: Maciej Krawczak
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-00248-4
Print ISBN: 978-3-319-00247-7
DOI: https://doi.org/10.1007/978-3-319-00248-4