Holographic Reduced Representation

Distributed Representation for Cognitive Structures

Tony A. Plate

Holographic Reduced Representation
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Tony A. Plate

Distributed for Center for the Study of Language and Information

250 pages | 6 x 9 | © 2003
Cloth $70.00 ISBN: 9781575864297 Published April 2003
Paper $27.00 ISBN: 9781575864303 Published April 2003
While neuroscientists garner success in identifying brain regions and in analyzing individual neurons, ground is still being broken at the intermediate scale of understanding how neurons combine to encode information. This book proposes a method of representing information in a computer that would be suited for modeling the brain's methods of processing information.

Holographic Reduced Representations (HRRs) are introduced here to model how the brain distributes each piece of information among thousands of neurons. It had been previously thought that the grammatical structure of a language cannot be encoded practically in a distributed representation, but HRRs can overcome the problems of earlier proposals. Thus this work has implications for psychology, neuroscience, linguistics, and computer science, and engineering.
1. Introduction
2. Review of connectionist and distributed memory models
3. Holographic Reduced Representation
4. HRRs in the frequency domain
5. Using convolution-based storage in systems that learn
6. Estimating analogical similarity
7. Discussion
Appendix A: Means and variances of similarities between bindings
Appendix B: The capacity of a superposition memory
Appendix C: A lower bound for the capacity of superposition memories
Appendix D: The capacity of convolution-based associative memories
Appendix E: A lower bound for the capacity of convolution memories
Appendix F: Means and variances of a signal
Appendix G: The effect of normalization on dot-products
Appendix H: HRRs with circular vectors
Appendix I: Arithmetic tables: an example of HRRs with many items in memory
Subject Index
Author Index
For more information, or to order this book, please visit http://www.press.uchicago.edu
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