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Circuit Complexity and Neural Networks

Author: Ian Parberry

Publisher: MIT Press

Published: 1994

Total Pages: 312

ISBN-13: 9780262161480

Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability. Most research in neural networks focuses on learning, yet it is important to understand the physical limitations of the network before the resources needed to solve a certain problem can be calculated. One of the aims of this book is to compare the complexity of neural networks and the complexity of conventional computers, looking at the computational ability and resources (neurons and time) that are a necessary part of the foundations of neural network learning. Circuit Complexity and Neural Networks contains a significant amount of background material on conventional complexity theory that will enable neural network scientists to learn about how complexity theory applies to their discipline, and allow complexity theorists to see how their discipline applies to neural networks.

Classes of Feedforward Neural Networks and Their Circuit Comlexity

Author: John Shawe-Taylor

Publisher:

Published: 1990

Total Pages: 24

ISBN-13:

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Neural Network Design and the Complexity of Learning

Author: J. Stephen Judd

Publisher: MIT Press

Published: 1990

Total Pages: 188

ISBN-13: 9780262100458

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Using the tools of complexity theory, Stephen Judd develops a formal description of associative learning in connectionist networks. He rigorously exposes the computational difficulties in training neural networks and explores how certain design principles will or will not make the problems easier.Judd looks beyond the scope of any one particular learning rule, at a level above the details of neurons. There he finds new issues that arise when great numbers of neurons are employed and he offers fresh insights into design principles that could guide the construction of artificial and biological neural networks.The first part of the book describes the motivations and goals of the study and relates them to current scientific theory. It provides an overview of the major ideas, formulates the general learning problem with an eye to the computational complexity of the task, reviews current theory on learning, relates the book's model of learning to other models outside the connectionist paradigm, and sets out to examine scale-up issues in connectionist learning.Later chapters prove the intractability of the general case of memorizing in networks, elaborate on implications of this intractability and point out several corollaries applying to various special subcases. Judd refines the distinctive characteristics of the difficulties with families of shallow networks, addresses concerns about the ability of neural networks to generalize, and summarizes the results, implications, and possible extensions of the work. Neural Network Design and the Complexity of Learning is included in the Network Modeling and Connectionism series edited by Jeffrey Elman.

Cellular Neural Networks

Author: Gabriele Manganaro

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 280

ISBN-13: 3642600441

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The field of cellular neural networks (CNNs) is of growing importance in non linear circuits and systems and it is maturing to the point of becoming a new area of study in general nonlinear theory. CNNs emerged through two semi nal papers co-authored by Professor Leon O. Chua back in 1988. Since then, the attention that CNNs have attracted in the scientific community has been vast. For instance, there are international workshops dedicated to CNNs and their applications, special issues published in both the International Journal of Circuit Theory and in the IEEE Transactions on Circuits and Systems, and there are also Associate Editors appointed in the latter journal especially for the CNN field. All of this bears witness the importance that CNNs are gaining within the scientific community. Without doubt this book is a primer in the field. Its extensive coverage provides the reader with a very comprehensive view of aspects involved in the theory and applications of cellular neural networks. The authors have done an excellent job merging basic CNN theory, synchronization, spatio temporal phenomena and hardware implementation into eight exquisitely written chapters. Each chapter is thoroughly illustrated with examples and case studies. The result is a book that is not only excellent as a professional reference but also very appealing as a textbook. My view is that students as well professional engineers will find this volume extremely useful.

Dealing with Complexity

Author: Mirek Karny

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 323

ISBN-13: 1447115236

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In almost all areas of science and engineering, the use of computers and microcomputers has, in recent years, transformed entire subject areas. What was not even considered possible a decade or two ago is now not only possible but is also part of everyday practice. As a result, a new approach usually needs to be taken (in order) to get the best out of a situation. What is required is now a computer's eye view of the world. However, all is not rosy in this new world. Humans tend to think in two or three dimensions at most, whereas computers can, without complaint, work in n dimensions, where n, in practice, gets bigger and bigger each year. As a result of this, more complex problem solutions are being attempted, whether or not the problems themselves are inherently complex. If information is available, it might as well be used, but what can be done with it? Straightforward, traditional computational solutions to this new problem of complexity can, and usually do, produce very unsatisfactory, unreliable and even unworkable results. Recently however, artificial neural networks, which have been found to be very versatile and powerful when dealing with difficulties such as nonlinearities, multivariate systems and high data content, have shown their strengths in general in dealing with complex problems. This volume brings together a collection of top researchers from around the world, in the field of artificial neural networks.

Introduction to Circuit Complexity

Author: Heribert Vollmer

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 277

ISBN-13: 3662039273

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An advanced textbook giving a broad, modern view of the computational complexity theory of boolean circuits, with extensive references, for theoretical computer scientists and mathematicians.

Neural Networks and Analog Computation

Author: Hava T. Siegelmann

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 193

ISBN-13: 146120707X

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The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics. The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.

Discrete Neural Computation

Author: Kai-Yeung Siu

Publisher: Prentice Hall

Published: 1995

Total Pages: 444

ISBN-13:

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Written by the three leading authorities in the field, this book brings together -- in one volume -- the recent developments in discrete neural computation, with a focus on neural networks with discrete inputs and outputs. It integrates a variety of important ideas and analytical techniques, and establishes a theoretical foundation for discrete neural computation. Discusses the basic models for discrete neural computation and the fundamental concepts in computational complexity; establishes efficient designs of threshold circuits for computing various functions; develops techniques for analyzing the computational power of neural models. A reference/text for computer scientists and researchers involved with neural computation and related disciplines.

Silicon Implementation of Pulse Coded Neural Networks

Author: Mona E. Zaghloul

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 293

ISBN-13: 1461526809

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When confronted with the hows and whys of nature's computational engines, some prefer to focus upon neural function: addressing issues of neural system behavior and its relation to natural intelligence. Then there are those who prefer the study of the "mechanics" of neural systems: the nuts and bolts of the "wetware": the neurons and synapses. Those who investigate pulse coded implementations ofartificial neural networks know what it means to stand at the boundary which lies between these two worlds: not just asking why natural neural systems behave as they do, but also how they achieve their marvelous feats. The research results presented in this book not only address more conventional abstract notions of neural-like processing, but also the more specific details ofneural-like processors. It has been established for some time that natural neural systems perform a great deal of information processing via electrochemical pulses. Accordingly, pulse coded neural network concepts are receiving increased attention in artificial neural network research. This increased interest is compounded by continuing advances in the field of VLSI circuit design. This is the first time in history in which it is practical to construct networks of neuron-like circuits of reasonable complexity that can be applied to real problems. We believe that the pioneering work in artificial neural systems presented in this book will lead to further advances that will not only be useful in some practical sense, but may also provide some additional insight into the operation of their natural counterparts.

Mathematical Perspectives on Neural Networks

Author: Paul Smolensky

Publisher: Psychology Press

Published: 2013-05-13

Total Pages: 890

ISBN-13: 1134773013

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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.