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Mathematical Methods for Neural Network Analysis and Design

1996 Computers
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Release : 1996
Genre : Computers
Kind : eBook
Book Rating : 741/5 ( reviews)

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Book Synopsis Mathematical Methods for Neural Network Analysis and Design by : Richard M. Golden

Download or read book Mathematical Methods for Neural Network Analysis and Design written by Richard M. Golden. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.

Mathematical Perspectives on Neural Networks

2013-05-13 Psychology
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Release : 2013-05-13
Genre : Psychology
Kind : eBook
Book Rating : 013/5 ( reviews)

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Book Synopsis Mathematical Perspectives on Neural Networks by : Paul Smolensky

Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky. This book was released on 2013-05-13. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.

Mathematical Approaches to Neural Networks

1993-10-27 Computers
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Release : 1993-10-27
Genre : Computers
Kind : eBook
Book Rating : 392/5 ( reviews)

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Book Synopsis Mathematical Approaches to Neural Networks by : J.G. Taylor

Download or read book Mathematical Approaches to Neural Networks written by J.G. Taylor. This book was released on 1993-10-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamics of Neural Networks

2020-12-18 Science
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Release : 2020-12-18
Genre : Science
Kind : eBook
Book Rating : 848/5 ( reviews)

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Book Synopsis Dynamics of Neural Networks by : Michel J.A.M. van Putten

Download or read book Dynamics of Neural Networks written by Michel J.A.M. van Putten. This book was released on 2020-12-18. Available in PDF, EPUB and Kindle. Book excerpt: This book treats essentials from neurophysiology (Hodgkin–Huxley equations, synaptic transmission, prototype networks of neurons) and related mathematical concepts (dimensionality reductions, equilibria, bifurcations, limit cycles and phase plane analysis). This is subsequently applied in a clinical context, focusing on EEG generation, ischaemia, epilepsy and neurostimulation. The book is based on a graduate course taught by clinicians and mathematicians at the Institute of Technical Medicine at the University of Twente. Throughout the text, the author presents examples of neurological disorders in relation to applied mathematics to assist in disclosing various fundamental properties of the clinical reality at hand. Exercises are provided at the end of each chapter; answers are included. Basic knowledge of calculus, linear algebra, differential equations and familiarity with MATLAB or Python is assumed. Also, students should have some understanding of essentials of (clinical) neurophysiology, although most concepts are summarized in the first chapters. The audience includes advanced undergraduate or graduate students in Biomedical Engineering, Technical Medicine and Biology. Applied mathematicians may find pleasure in learning about the neurophysiology and clinic essentials applications. In addition, clinicians with an interest in dynamics of neural networks may find this book useful, too.

Deep Learning Architectures

2020-02-13 Mathematics
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Release : 2020-02-13
Genre : Mathematics
Kind : eBook
Book Rating : 215/5 ( reviews)

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Book Synopsis Deep Learning Architectures by : Ovidiu Calin

Download or read book Deep Learning Architectures written by Ovidiu Calin. This book was released on 2020-02-13. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

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