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| Author | : Jia-Bao Liu |
| Publisher | : Frontiers Media SA |
| Total Pages | : 239 |
| Release | : 2021-12-03 |
| Genre | : Science |
| ISBN | : 2889717976 |
| Author | : Martin Anthony |
| Publisher | : SIAM |
| Total Pages | : 137 |
| Release | : 2001-01-01 |
| Genre | : Computers |
| ISBN | : 089871480X |
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 | : J.G. Taylor |
| Publisher | : Elsevier |
| Total Pages | : 381 |
| Release | : 1993-10-27 |
| Genre | : Computers |
| ISBN | : 9780080887395 |
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 | : Jianhong Wu |
| Publisher | : Walter de Gruyter |
| Total Pages | : 200 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9783110169881 |
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 | : Anthony L. Caterini |
| Publisher | : Springer |
| Total Pages | : 84 |
| Release | : 2018-03-22 |
| Genre | : Computers |
| ISBN | : 3319753045 |
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 | : Neha Yadav |
| Publisher | : Springer |
| Total Pages | : 124 |
| Release | : 2015-02-26 |
| Genre | : Mathematics |
| ISBN | : 9401798168 |
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 | : Steve Ellacott |
| Publisher | : Itp New Media |
| Total Pages | : 414 |
| Release | : 1996 |
| Genre | : Computers |
| ISBN | : |
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.
| Author | : Seoyun J. Kwon |
| Publisher | : Nova Science Publishers |
| Total Pages | : 426 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9781617616976 |
| Author | : Kevin Gurney |
| Publisher | : CRC Press |
| Total Pages | : 248 |
| Release | : 1997-08-05 |
| Genre | : Computers |
| ISBN | : 9781857286731 |
Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.
| Author | : Christian Constanda |
| Publisher | : Springer |
| Total Pages | : 478 |
| Release | : 2019-07-18 |
| Genre | : Mathematics |
| ISBN | : 3030160777 |
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
