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Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors

Abstract

The 1990s saw the emergence of cognitive models that depend on very high dimensionality and randomness. They include Holographic Reduced Representations, Spatter Code, Semantic Vectors, Latent Semantic Analysis, Context-Dependent Thinning, and Vector-Symbolic Architecture. They represent things in high-dimensional vectors that are manipulated by operations that produce new high-dimensional vectors in the style of traditional computing, in what is called here hyperdimensional computing on account of the very high dimensionality. The paper presents the main ideas behind these models, written as a tutorial essay in hopes of making the ideas accessible and even provocative. A sketch of how we have arrived at these models, with references and pointers to further reading, is given at the end. The thesis of the paper is that hyperdimensional representation has much to offer to students of cognitive science, theoretical neuroscience, computer science and engineering, and mathematics.

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Acknowledgements

Real Wold Computing Project funding by Japan’s Ministry of International Trade and Industry to the Swedish Institute of Computer Science in 1994–2001 made it possible for us to develop the ideas for high-dimensional binary representation. The support of Dr. Nobuyuki Otsu throughout the project was most valuable. Dr. Dmitri Rachkovskij provided information on early use of permutations to encode sequences by researchers in Ukraine. Dikran Karagueuzian of CSLI Publications accepted for publication Plate’s book on Holographic Reduced Representation after a publishing agreement elsewhere fell through. Discussions with Tony Plate and Ross Gayler have helped shape the ideas and their presentation here. Sincere thanks to you all, as well as to my coauthors on papers on representation and to three anonymous reviewers of the manuscript.

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Correspondence to Pentti Kanerva.

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Kanerva, P. Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors. Cogn Comput 1, 139–159 (2009). https://doi.org/10.1007/s12559-009-9009-8

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Keywords

  • Holographic reduced representation
  • Holistic record
  • Holistic mapping
  • Random indexing
  • Cognitive code
  • von Neumann architecture