Holographic reduced representations
Abstract
Associative memories are conventionally used to represent data with very simple structure: sets of pairs of vectors. This paper describes a method for representing more complex compositional structure in distributed representations. The method uses circular convolution to associate items, which are represented by vectors. Arbitrary variable bindings, short sequences of various lengths, simple frame-like structures, and reduced representations can be represented in a fixed width vector. These representations are items in their own right and can be used in constructing compositional structures. The noisy reconstructions extracted from convolution memories can be cleaned up by using a separate associative memory that has good reconstructive properties.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Vector symbolic architectures are being considered in the context of efficiently-trainable artificial neural networks; these systems learn how to use variable binding.
“Some, such as vector symbolic architectures53, which were proposed in cognitive science (Plate, 1995; Stewart and Eliasmith, 2009; Eliasmith, 2013), are also being considered in the context of efficiently-trainable artificial neural networks (Danihelka et al., 2016)—in effect, these systems learn how to use variable binding.”
From Toward an integration of deep learning and neuroscience (2016) · cites this paper as Plate, 1995
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270 · see citing works
Learning Internal Representations by Error Propagation
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1985) · doi:10.21236/ada164453 · Cited by 16,501 · see citing works
Parallel Distributed Processing: Explorations in the Microstructure of Cognition: Foundations
Rumelhart, D. E., McClelland, J. L., & AU (1986) · doi:10.7551/mitpress/5236.001.0001 · Cited by 15,686 · see citing works
Connectionism and cognitive architecture: A critical analysis
Fodor, J. A., & Pylyshyn, Z. W. (1988) · Cognition · doi:10.1016/0010-0277(88)90031-5 · Cited by 4,022 · see citing works
Parallel models of associative memory
Heath, R. A. (1982) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(82)90036-0 · Cited by 1,111 · see citing works
Brigham, E. O., & Yuen, C. K. (1978) · IEEE Transactions on Systems Man and Cybernetics · doi:10.1109/tsmc.1978.4309919 · Cited by 1,039 · see citing works
Hinton, G. E. (2018) · KiltHub Repository · doi:10.1184/r1/6604925 · Cited by 1,029 · see citing works
Kanerva, P. (1988) · Medical Entomology and Zoology · Cited by 967 · see citing works
Smolensky, P. (1990) · Artificial Intelligence · doi:10.1016/0004-3702(90)90007-m · Cited by 959 · see citing works
A theory for the storage and retrieval of item and associative information.
Murdock, B. B. (1982) · Psychological Review · doi:10.1037/0033-295x.89.6.609 · Cited by 927 · see citing works
Recursive distributed representations
Pollack, J. B. (1990) · Artificial Intelligence · doi:10.1016/0004-3702(90)90005-k · Cited by 848 · see citing works
Lewandowsky, S., & Murdock, B. B. (1989) · Psychological Review · doi:10.1037/0033-295x.96.1.25 · Cited by 471 · see citing works
A composite holographic associative recall model.
Eich, J. M. (1982) · Psychological Review · doi:10.1037/0033-295x.89.6.627 · Cited by 396 · see citing works
Ahmed, N., & Rao, K. R. (1975) · Springer eBooks · doi:10.1007/978-3-642-45450-9_4 · Cited by 369 · see citing works
On the complex backpropagation algorithm
Benvenuto, N., & Piazza, F. (1992) · IEEE Transactions on Signal Processing · doi:10.1109/78.127967 · Cited by 319 · see citing works
Mapping part-whole hierarchies into connectionist networks
Hinton, G. E. (1990) · Artificial Intelligence · doi:10.1016/0004-3702(90)90004-j · Cited by 307 · see citing works
A Distributed Connectionist Production System
Touretzky, D. S., & Hinton, G. E. (1988) · Cognitive Science · doi:10.1207/s15516709cog1203_4 · Cited by 287 · see citing works
Gabel, R. A., & Roberts, R. A. (1973) · CERN Document Server (European Organization for Nuclear Research) · Cited by 223 · see citing works
A distributed memory model for serial-order information.
Murdock, B. B. (1983) · Psychological Review · doi:10.1037/0033-295x.90.4.316 · Cited by 199 · see citing works
Optimal Plasticity from Matrix Memories: What Goes Up Must Come Down
Willshaw, D. J., & Dayan, P. (1990) · Neural Computation · doi:10.1162/neco.1990.2.1.85 · Cited by 190 · see citing works
Handbook of digital signal processing: engineering applications
(1988) · Choice Reviews Online · doi:10.5860/choice.26-0940 · Cited by 164 · see citing works
Pike, R. (1984) · Psychological Review · doi:10.1037/0033-295x.91.3.281 · Cited by 155 · see citing works
Optical Associative Memory Using Fourier Transform Holograms
Paek, E. G., & Psaltis, D. (1987) · Optical Engineering · doi:10.1117/12.7974093 · Cited by 136 · see citing works
BoltzCONS: Dynamic symbol structures in a connectionist network
Touretzky, D. S. (1990) · Artificial Intelligence · doi:10.1016/0004-3702(90)90003-i · Cited by 116 · see citing works
Optical implementations of associative networks with versatile adaptive learning capabilities
Fisher, A. D., Lippincott, W. L., & Lee, J. N. (1987) · Applied Optics · doi:10.1364/ao.26.005039 · Cited by 91 · see citing works
A distributed connectionist representation for concept structures
Touretzky, D. S., Geva, S., & Project., A. I. A. P. (2018) · Figshare · doi:10.1184/r1/6587366 · Cited by 74 · see citing works
Convolution and correlation algebras
Borsellino, A., & Poggio, T. (1973) · Kybernetik · doi:10.1007/bf00288790 · Cited by 68 · see citing works
Principles for an Integrated Connectionist/Symbolic Theory of Higher Cognition ; CU-CS-600-92
Smolensky, P., Légendre, G., & Miyata, Y. (1992) · CU Scholar (University of Colorado Boulder) · Cited by 50 · see citing works
Schönemann, P. H. (2008) · Biological Cybernetics · doi:10.1007/s00422-008-0223-3 · Cited by 35 · see citing works
Weber, E. U. (1988) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(88)90036-3 · Cited by 35 · see citing works
Schönemann, P. H. (1987) · Biological Cybernetics · doi:10.1007/bf00319516 · Cited by 34 · see citing works
Holographic Recurrent Networks
Plate, T. A. (1992) · Cited by 32 · see citing works
Self-citationOn holographic models of memory
Poggio, T. (1973) · Kybernetik · doi:10.1007/bf00270577 · Cited by 25 · see citing works
Key and recollection vector effects on heteroassociative memory performance
Casasent, D. P., & Telfer, B. A. (1989) · Applied Optics · doi:10.1364/ao.28.000272 · Cited by 19 · see citing works
Coarse-Coded Symbol Memories and Their Properties
Rosenfeld, R., & Touretzky, D. S. (1988) · Figshare · doi:10.1184/r1/21709595 · Cited by 13 · see citing works
A parsing architecture based on distributed memory machines
Slack, J. M. (1984) · Annual Meeting of the Association for Computational Linguistics (ACL) · doi:10.3115/980491.980513 · Cited by 5 · see citing works
A parsing architecture based on distributed memory machines
Slack, J. M. (1984) · International Conference on Computational Linguistics · doi:10.3115/980431.980513 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- -i e , a o rithm," IEEE Trans. Signal Processing, vol. 40, no. 4, pp. 967–969, 1992.
- [6]P. J. Davis. Circulant Matrices. New York: Wiley, 1979.
- [21]—, "Serial-order effects in a distributed-memory model," in Memory and Learning: The Ebbinghaus Centennial Conference, D. S. Gorfein and R. R. Hoffman, Eds. Hillsdale, NJ: Erlbaum, 1987, pp. 277–310.. - ,
- [23]R. Pike, "Comparison of convolution and matrix distributed memory yscnl yonl soil nl sl sc l ssies vol. 91, no. 3, pp. 281–294, 1984.
Cited by
Sorted by citations
Knowledge Graph Embedding: A Survey of Approaches and Applications
Wang, Q., Mao, Z., Wang, B., & Guo, L. (2017) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2017.2754499 · Cited by 2,654 · see citing works
Neural reuse: A fundamental organizational principle of the brain
Anderson, M. L. (2010) · Behavioral and Brain Sciences · doi:10.1017/s0140525x10000853 · Cited by 1,212 · see citing works
Dehaene, S., Meyniel, F., Wacongne, C., Wang, L., & Pallier, C. (2015) · Neuron · doi:10.1016/j.neuron.2015.09.019 · Cited by 478 · see citing works
Neurophysiological dynamics of phrase-structure building during sentence processing
Nelson, M. J., El Karoui, I., Giber, K., Yang, X., Cohen, L., Koopman, H., Cash, S. S., Naccache, L., Hale, J. T., Pallier, C., et al. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1701590114 · Cited by 319 · see citing works
Classification using hyperdimensional computing: a review
Ge, L., & Parhi, K. K. (2020) · IEEE Circuits and Systems Magazine · doi:10.1109/mcas.2020.2988388 · Cited by 227 · see citing works
Indirection and symbol-like processing in the prefrontal cortex and basal ganglia
Kriete, T., Noelle, D. C., Cohen, J. D., & O’Reilly, R. C. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1303547110 · Cited by 181 · see citing works
Cognitive Control: Core Constructs and Current Considerations
Cohen, J. D. (2017) · The Wiley Handbook of Cognitive Control · doi:10.1002/9781118920497.ch1 · Cited by 179 · see citing works
Toward an integration of deep learning and neuroscience
Marblestone, A. H., Wayne, G., & Kording, K. P. (2016) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2016.00094 · Cited by 119 · see citing works
On the Binding Problem in Artificial Neural Networks
Greff, K., van Steenkiste, S., & Schmidhuber, J. (2020) · arXiv · doi:10.48550/arxiv.2012.05208 · Cited by 102 · see citing works
- Authors
- Plate, T. A.
- Affiliations
- BC Cancer Agency (CA)
- Corresponding author
- Plate, T.A.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1995-05
- Volume
- 6
- Issue
- 3
- Pages
- 623-641
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W2157306293
- Cited by
- 657
- References
- 37
- Citations by year
- 2026: 26 · 2025: 57 · 2024: 37 · 2023: 24 · 2022: 38 · 2021: 43 · 2020: 50 · 2019: 69 · 2018: 32 · 2017: 23 · 2016: 23 · 2015: 14 · 2014: 30 · 2013: 17 · 2012: 25
- FWCI
- 5.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Cognitive Computing and Networks
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Keywords
- holographic reduced representations, associative memory, circular convolution, distributed representations, compositional structure, variable binding
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
