References

Academic papers and resources foundational to HoloVec.

Foundational Works

Kanerva, P. (1988). Sparse Distributed Memory. MIT Press.

• Introduced sparse distributed memory concepts
• Foundation for BSDC models

Plate, T. A. (1995). Holographic Reduced Representations: Distributed representation for cognitive structures. Artificial Intelligence, 75(1), 107-140.

• Introduced HRR model
• Circular convolution binding

Plate, T. A. (2003). Holographic Reduced Representations: Distributed Representation for Cognitive Structures. CSLI Publications.

• Comprehensive treatment of HRR
• Capacity analysis, applications

Gayler, R. W. (2003). Vector Symbolic Architectures answer Jackendoff's challenges for cognitive neuroscience. Proceedings of ICCS/ASCS.

• Coined "Vector Symbolic Architecture"
• Relationship to cognitive science

Model-Specific Papers

FHRR

Plate, T. A. (2003). (See above)

• FHRR as complex-valued HRR variant

MAP

Kanerva, P. (2009). Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors. Cognitive Computation, 1(2), 139-159.

• Introduced MAP model
• Tutorial introduction to HDC

BSC

Kanerva, P. (1996). Binary Spatter-Coding of Ordered K-Tuples. Proceedings of ICANN.

• Introduced binary spatter codes
• Sequence encoding

BSDC

Rachkovskij, D. A., & Kussul, E. M. (2001). Binding and normalization of binary sparse distributed representations by context-dependent thinning. Neural Computation, 13(2), 411-452.

• Sparse binary codes
• Context-dependent binding

GHRR

Yeung, W., Zou, A., & Imani, F. (2024). Generalized Holographic Reduced Representations. arXiv:2405.09689.

• Extended HRR to matrix domain
• Non-commutative binding
• State-of-the-art 2024

VTB

Gallant, S. I., & Okaywe, T. W. (2013). Representing Objects, Relations, and Sequences. Neural Computation, 25(8), 2038-2078.

• Matrix Binding of Additive Terms (MBAT)
• Non-commutative binding approach

Encoders

Fractional Power Encoding

Frady, E. P., Kleyko, D., & Sommer, F. T. (2021). Computing on Functions Using Randomized Vector Representations. arXiv:2109.03429.

• VFA framework
• Fractional power encoding theory
• Kernel interpretation

Surveys and Comparisons

Schlegel, K., Neubert, P., & Protzel, P. (2022). A comparison of vector symbolic architectures. Artificial Intelligence Review, 55(4), 2583-2647.

• Comprehensive model comparison
• Capacity analysis
• Benchmark results

Kleyko, D., Rachkovskij, D. A., Osipov, E., & Rahimi, A. (2023). A Survey on Hyperdimensional Computing: Theory, Algorithms, and Applications. ACM Computing Surveys, 55(6), 1-45.

• Comprehensive HDC/VSA survey
• Applications overview
• Future directions

Cleanup and Retrieval

Kymn, C. J., Frady, E. P., & Sommer, F. T. (2024). Resonator Networks for Learning Compositional Representations. arXiv:2404.18789.

• Resonator networks
• Iterative factorization
• Superior to brute force cleanup

Applications

Rahimi, A., et al. (2019). High-Dimensional Computing as a Nanoscalable Paradigm. IEEE Transactions on Circuits and Systems I, 66(11), 4266-4278.

• Hardware implementation
• Neuromorphic computing

Mitrokhin, A., Sutor, P., Fermüller, C., & Aloimonos, Y. (2019). Learning sensorimotor control with neuromorphic sensors: Toward hyperdimensional active perception. Science Robotics, 4(30).

• Robotics application
• Event-based sensing

Biological Foundations

Kanerva, P. (1993). Sparse distributed memory and related models. Associative Neural Memories, 50-76.

• Biological plausibility
• Connection to neural coding

Books

Kanerva, P. (1988). Sparse Distributed Memory. MIT Press.

• Foundational text

Plate, T. A. (2003). Holographic Reduced Representations. CSLI Publications.

• Complete HRR treatment

Eliasmith, C., & Anderson, C. H. (2003). Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems. MIT Press.

• Neural perspective on VSA

Online Resources

• HoloVec GitHub — This library
• HDC/VSA Community — Research community
• Penn Kanerva Group — Foundational research

Citation

If you use HoloVec in your research:

@software{HoloVec2025,
  author       = {Brodie Schroeder},
  title        = {HoloVec: Vector Symbolic Architectures for Python},
  year         = {2025},
  version      = {0.1.1},
  url          = {https://github.com/Twistient/HoloVec},
  license      = {Apache-2.0}
}

See Also

• Core Concepts — Mathematical foundations
• Models — Implementation details
• Glossary — Term definitions