# A comparison of Vector Symbolic Architectures

arXiv: https://arxiv.org/abs/2001.11797 · HTML: https://mlsanity.com/paper/2001.11797/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 30 of 64)

- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Vector Symbolic Architectures as a Computing Framework for Emerging Hardware](https://mlsanity.com/paper/2106.05268/) (2021)
- [Hyperdimensional computing as a framework for systematic aggregation of image descriptors](https://mlsanity.com/paper/2101.07720/) (2021)
- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [Learning with Holographic Reduced Representations](https://mlsanity.com/paper/2109.02157/) (2021)
- [Relational Composition in Neural Networks: A Survey and Call to Action](https://mlsanity.com/paper/2407.14662/) (2024)
- [Understanding Hyperdimensional Computing for Parallel Single-Pass Learning](https://mlsanity.com/paper/2202.04805/) (2022)
- [Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architectures](https://mlsanity.com/paper/2205.09208/) (2022)
- [HDC-MiniROCKET: Explicit Time Encoding in Time Series Classification with Hyperdimensional Computing](https://mlsanity.com/paper/2202.08055/) (2022)
- [Hyperdimensional Feature Fusion for Out-Of-Distribution Detection](https://mlsanity.com/paper/2112.05341/) (2021)
- [Unpaired Image Translation via Vector Symbolic Architectures](https://mlsanity.com/paper/2209.02686/) (2022)
- [Learning from Hypervectors: A Survey on Hypervector Encoding](https://mlsanity.com/paper/2308.00685/) (2023)
- [Generalized Holographic Reduced Representations](https://mlsanity.com/paper/2405.09689/) (2024)
- [Hyperdimensional Uncertainty Quantification for Multimodal Uncertainty Fusion in Autonomous Vehicles Perception](https://mlsanity.com/paper/2503.20011/) (2025)
- [Exploring Effects of Hyperdimensional Vectors for Tsetlin Machines](https://mlsanity.com/paper/2406.02648/) (2024)
- [Deep Phasor Networks: Connecting Conventional and Spiking Neural Networks](https://mlsanity.com/paper/2106.11908/) (2021)
- [Shift-Equivariant Similarity-Preserving Hypervector Representations of Sequences](https://mlsanity.com/paper/2112.15475/) (2021)
- [Factorizers for Distributed Sparse Block Codes](https://mlsanity.com/paper/2303.13957/) (2023)
- [Towards Generalization in Subitizing with Neuro-Symbolic Loss using Holographic Reduced Representations](https://mlsanity.com/paper/2312.15310/) (2023)
- [Laplace-HDC: Understanding the geometry of binary hyperdimensional computing](https://mlsanity.com/paper/2404.10759/) (2024)
- [A Walsh Hadamard Derived Linear Vector Symbolic Architecture](https://mlsanity.com/paper/2410.22669/) (2024)
- [Bridge Networks: Relating Inputs through Vector-Symbolic Manipulations](https://mlsanity.com/paper/2106.08446/) (2021)
- [Lempel-Ziv Networks](https://mlsanity.com/paper/2211.13250/) (2022)
- [Capacity Analysis of Vector Symbolic Architectures](https://mlsanity.com/paper/2301.10352/) (2023)
- [HDCC: A Hyperdimensional Computing compiler for classification on embedded systems and high-performance computing](https://mlsanity.com/paper/2304.12398/) (2023)
- [HEAL: Brain-inspired Hyperdimensional Efficient Active Learning](https://mlsanity.com/paper/2402.11223/) (2024)
- [Hyperdimensional Probe: Decoding LLM Representations via Vector Symbolic Architectures](https://mlsanity.com/paper/2509.25045/) (2025)
- [Recursive Binding for Similarity-Preserving Hypervector Representations of Sequences](https://mlsanity.com/paper/2201.11691/) (2022)
- [Optimal quadratic binding for relational reasoning in vector symbolic neural architectures](https://mlsanity.com/paper/2204.07186/) (2022)

## Abstract (arXiv)

Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their representational power and ability to deal with fuzziness and ambiguity. Over the past years, several VSA implementations have been proposed. The available implementations differ in the underlying vector space and the particular implementations of the VSA operators. This paper provides an overview of eleven available VSA implementations and discusses their commonalities and differences in the underlying vector space and operators. We create a taxonomy of available binding operations and show an important ramification for non self-inverse binding operations using an example from analogical reasoning. A main contribution is the experimental comparison of the available implementations in order to evaluate (1) the capacity of bundles, (2) the approximation quality of non-exact unbinding operations, (3) the influence of combining binding and bundling operations on the query answering performance, and (4) the performance on two example applications: visual place- and language-recognition. We expect this comparison and systematization to be relevant for development of VSAs, and to support the selection of an appropriate VSA for a particular task. The implementations are available.