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Author : Jia-Bao Liu,Muhammad Javaid,Shaohui Wang,Jinde Cao
Publisher : Frontiers Media SA
Page : 239 pages
File Size : 51,9 Mb
Release : 2021-12-03
Category : Science
ISBN : 9782889717972
Author : Martin Anthony
Publisher : SIAM
Page : 137 pages
File Size : 49,7 Mb
Release : 2001-01-01
Category : Computers
ISBN : 9780898714807
This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.
Author : Anthony L. Caterini,Dong Eui Chang
Publisher : Springer
Page : 84 pages
File Size : 49,8 Mb
Release : 2018-03-22
Category : Computers
ISBN : 9783319753041
This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks. This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.
Author : Jianhong Wu
Publisher : Walter de Gruyter
Page : 200 pages
File Size : 49,8 Mb
Release : 2001
Category : Mathematics
ISBN : 3110169886
In the design of a neural network, either for biological modeling, cognitive simulation, numerical computation or engineering applications, it is important to investigate the network's computational performance which is usually described by the long-term behaviors, called dynamics, of the model equations. The purpose of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons from the viewpoint of dynamical systems.
Author : Marat Akhmet,Enes Yılmaz
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 45,8 Mb
Release : 2013-10-30
Category : Technology & Engineering
ISBN : 9781461485667
This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.
Author : J.G. Taylor
Publisher : Elsevier
Page : 381 pages
File Size : 50,8 Mb
Release : 1993-10-27
Category : Computers
ISBN : 0080887392
The subject of Neural Networks is being seen to be coming of age, after its initial inception 50 years ago in the seminal work of McCulloch and Pitts. It is proving to be valuable in a wide range of academic disciplines and in important applications in industrial and business tasks. The progress being made in each approach is considerable. Nevertheless, both stand in need of a theoretical framework of explanation to underpin their usage and to allow the progress being made to be put on a firmer footing. This book aims to strengthen the foundations in its presentation of mathematical approaches to neural networks. It is through these that a suitable explanatory framework is expected to be found. The approaches span a broad range, from single neuron details to numerical analysis, functional analysis and dynamical systems theory. Each of these avenues provides its own insights into the way neural networks can be understood, both for artificial ones and simplified simulations. As a whole, the publication underlines the importance of the ever-deepening mathematical understanding of neural networks.
Author : Neha Yadav,Anupam Yadav,Manoj Kumar
Publisher : Springer
Page : 114 pages
File Size : 44,7 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9789401798167
This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.
Author : Seoyun J. Kwon
Publisher : Nova Science Publishers
Page : 426 pages
File Size : 50,6 Mb
Release : 2011
Category : Mathematics
ISBN : 1617616974
Author : Anton Bovier,Pierre Picco
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241027
Author : Anthony Michel,Derong Liu
Publisher : CRC Press
Page : 504 pages
File Size : 40,6 Mb
Release : 2001-12-04
Category : Mathematics
ISBN : 9781482275780
"Analyzes the behavior, design, and implementation of artificial recurrent neural networks. Offers methods of synthesis for associative memories. Evaluates the qualitative properties and limitations of neural networks. Contains practical applications for optimal system performance."
Author : Gérard Dreyfus
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 55,5 Mb
Release : 2005-11-25
Category : Science
ISBN : 9783540288473
Neural networks represent a powerful data processing technique that has reached maturity and broad application. When clearly understood and appropriately used, they are a mandatory component in the toolbox of any engineer who wants make the best use of the available data, in order to build models, make predictions, mine data, recognize shapes or signals, etc. Ranging from theoretical foundations to real-life applications, this book is intended to provide engineers and researchers with clear methodologies for taking advantage of neural networks in industrial, financial or banking applications, many instances of which are presented in the book. For the benefit of readers wishing to gain deeper knowledge of the topics, the book features appendices that provide theoretical details for greater insight, and algorithmic details for efficient programming and implementation. The chapters have been written by experts and edited to present a coherent and comprehensive, yet not redundant, practically oriented introduction.
Author : Daniel Graupe
Publisher : World Scientific
Page : 256 pages
File Size : 53,5 Mb
Release : 1997-05-01
Category : Mathematics
ISBN : 9810241259
This textbook is intended for a first-year graduate course on Artificial Neural Networks. It assumes no prior background in the subject and is directed to MS students in electrical engineering, computer science and related fields, with background in at least one programming language or in a programming tool such as Matlab, and who have taken the basic undergraduate classes in systems or in signal processing.
Author : S. Chakraverty,Susmita Mall
Publisher : CRC Press
Page : 169 pages
File Size : 55,7 Mb
Release : 2017-07-20
Category : Mathematics
ISBN : 9781498781404
Differential equations play a vital role in the fields of engineering and science. Problems in engineering and science can be modeled using ordinary or partial differential equations. Analytical solutions of differential equations may not be obtained easily, so numerical methods have been developed to handle them. Machine intelligence methods, such as Artificial Neural Networks (ANN), are being used to solve differential equations, and these methods are presented in Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations. This book shows how computation of differential equation becomes faster once the ANN model is properly developed and applied.
Author : Bruno Després
Publisher : Walter de Gruyter GmbH & Co KG
Page : 177 pages
File Size : 41,7 Mb
Release : 2022-08-22
Category : Mathematics
ISBN : 9783110783261
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.
Author : Steve Ellacott,Deb Bose
Publisher : Itp New Media
Page : 414 pages
File Size : 49,5 Mb
Release : 1996
Category : Computers
ISBN : UOM:39015038575273
Neural networks provide a powerful approach to problems of machine learning and pattern recognition. the underlying mathematics, however, has much more in common with classical applied mathematics. This book introduces teh deterministic aspects of the mathematical theory in a comprehensive way.