Mathematical Perspectives on Neural Networks / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$227.08
Used and New from Other Sellers
Used and New from Other Sellers
from $40.00
Usually ships in 1-2 business days
(Save 84%)
Other sellers (Hardcover)
  • All (8) from $40.00   
  • New (3) from $59.99   
  • Used (5) from $40.00   

Overview

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.

Read More Show Less

Product Details

Table of Contents

Contents: Preface: Multilayer Structure of the Book and Its Summaries. P. Smolensky, Overview: Computational, Dynamical, and Statistical Perspectives on the Processing and Learning Problems in Neural Network Theory. Part I: Computational Perspectives. P. Smolensky, Overview: Computational Perspectives on Neural Networks. S. Franklin, M. Garzon, Computation by Discrete Neural Nets. I. Parberry, Circuit Complexity and Feedforward Neural Networks. J.S. Judd, Complexity of Learning. E.H.L Aarts, J.H.M. Korst, P.J. Zwietering, Deterministic and Randomized Local Search. M.B. Pour-El, The Mathematical Theory of the Analog Computer. Part II: Dynamical Perspectives. P. Smolensky, Overview: Dynamical Perspectives on Neural Networks. M.W. Hirsch, Dynamical Systems. L.F. Abbott, Statistical Analysis of Neural Networks. K.S. Narendra, S-M. Li, Neural Networks in Control Systems. A.S. Weigend, Time Series Analysis and Prediction. Part III: Statistical Perspectives. P. Smolensky, Overview: Statistical Perspectives on Neural Networks. R. Szeliski, Regularization in Neural Nets. D.E. Rumelhart, R. Durbin, R. Goldin, Y. Chauvin, Backpropagation: The Basic Theory. J. Rissanen, Information Theory and Neural Nets. A. Nádas, R.L. Mercer, Hidden Markov Models and Some Connections with Artificial Neural Nets. D. Haussler, Probably Approximately Correct Learning and Decision-Theoretic Generalizations. H. White, Parametric Statistical Estimation with Artificial Neural Networks. V.N. Vapnik, Inductive Principles of Statistics and Learning Theory.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)