Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

1 Overview: Computational, Dynamical, and Statistical Perspectives on the Processing and Learning Problems in Neural Network Theory

Paul Smolensky Johns Hopkins University

A neural network is a collection of interconnected elements or units. Beyond that nearly trivial characterization, the phrase neural network means an amazing variety of things to a remarkable diversity of researchers. For biologists, of course, it refers to a mass of grey matter or, perhaps, a biologically faithful model of some part of the brain. For psychologists and other cognitive scientists, 'neural' (or 'connectionist') network denotes a virtual machine architecture that has come to be seriously considered as a model of the mind. In this book, however, we put aside neuroscience and cognitive science, and regard a neural network as a purely formal object--or better, as a rich family of formal objects. For even narrowing our scope to purely mathematical perspectives, 'neural network' still has a striking diversity of construals. For example, the following perspectives are all represented in this book (the terms used will all be defined several times throughout the book, at multiple levels of detail).

To a theoretical computer scientist, 'neural network' is likely to mean a network of threshold logic gates, the central issues including: which Boolean functions can be computed, how quickly the number of gates needed grows with the size of the input, and the difficulty of the problem of determining whether a given function can be computed by a given family of networks.

But to some computer scientists, a neural network is a Markov process, evolving through time in a stochastic search for globally optimal states. And to still others, a neural network is a collection of analog devices, continuously evolving in time under the direction of certain differential equations.

To a physicist, a neural network may be a dynamical system evolving in time toward attractors of various types, or it might be a low-level substrate over which large-scale average behavior can be studied in the manner of statistical mechanics.

-1-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Mathematical Perspectives on Neural Networks
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 864

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.