# Understanding Hyperdimensional Computing for Parallel Single-Pass Learning

arXiv: https://arxiv.org/abs/2202.04805 · HTML: https://mlsanity.com/paper/2202.04805/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [Classification using Hyperdimensional Computing: A Review](https://mlsanity.com/paper/2004.11204/) (2020)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Hyperdimensional computing as a framework for systematic aggregation of image descriptors](https://mlsanity.com/paper/2101.07720/) (2021)
- [A theory of sequence indexing and working memory in recurrent neural networks](https://mlsanity.com/paper/1803.00412/) (2018)
- [Representing Objects, Relations, and Sequences](https://mlsanity.com/paper/1501.07627/) (2015)
- [Hypervector Design for Efficient Hyperdimensional Computing on Edge Devices](https://mlsanity.com/paper/2103.06709/) (2021)
- [Holographic Graph Neuron: a Bio-Inspired Architecture for Pattern Processing](https://mlsanity.com/paper/1501.03784/) (2015)

## Built on by (most cited first, 20 of 20)

- [LeHDC: Learning-Based Hyperdimensional Computing Classifier](https://mlsanity.com/paper/2203.09680/) (2022)
- [Learning from Hypervectors: A Survey on Hypervector Encoding](https://mlsanity.com/paper/2308.00685/) (2023)
- [Computing with Residue Numbers in High-Dimensional Representation](https://mlsanity.com/paper/2311.04872/) (2023)
- [Hyperdimensional Uncertainty Quantification for Multimodal Uncertainty Fusion in Autonomous Vehicles Perception](https://mlsanity.com/paper/2503.20011/) (2025)
- [An Encoding Framework for Binarized Images using HyperDimensional Computing](https://mlsanity.com/paper/2312.00454/) (2023)
- [Exploring Effects of Hyperdimensional Vectors for Tsetlin Machines](https://mlsanity.com/paper/2406.02648/) (2024)
- [Laplace-HDC: Understanding the geometry of binary hyperdimensional computing](https://mlsanity.com/paper/2404.10759/) (2024)
- [MetaLDC: Meta Learning of Low-Dimensional Computing Classifiers for Fast On-Device Adaption](https://mlsanity.com/paper/2302.12347/) (2023)
- [Resource-Efficient Federated Hyperdimensional Computing](https://mlsanity.com/paper/2306.01339/) (2023)
- [Efficient Hyperdimensional Computing](https://mlsanity.com/paper/2301.10902/) (2023)
- [Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products](https://mlsanity.com/paper/2506.15793/) (2025)
- [Bridging the Gap Between Hyperdimensional Computing and Kernel Methods via the Nystr"om Method](https://mlsanity.com/paper/2608.06860/) (2026)
- [Towards Vector Optimization on Low-Dimensional Vector Symbolic Architecture](https://mlsanity.com/paper/2502.14075/) (2025)
- [FactorHD: A Hyperdimensional Computing Model for Multi-Object Multi-Class Representation and Factorization](https://mlsanity.com/paper/2507.12366/) (2025)
- [Large-Margin Hyperdimensional Computing: A Learning-Theoretical Perspective](https://mlsanity.com/paper/2603.03830/) (2026)
- [HD-Bind: Encoding of Molecular Structure with Low Precision, Hyperdimensional Binary Representations](https://mlsanity.com/paper/2303.15604/) (2023)
- [CiliaGraph: Enabling Expression-enhanced Hyper-Dimensional Computation in Ultra-Lightweight and One-Shot Graph Classification on Edge](https://mlsanity.com/paper/2405.19033/) (2024)
- [ConformalHDC: Uncertainty-Aware Hyperdimensional Computing with Application to Neural Decoding](https://mlsanity.com/paper/2602.21446/) (2026)
- [Recursive Binding on a Budget: Subspace Carving in Order-p Tensor Memories](https://mlsanity.com/paper/2606.11391/) (2026)
- [Vector Symbolic Policy Gradient](https://mlsanity.com/paper/2608.18404/) (2026)

## Abstract (arXiv)

Hyperdimensional computing (HDC) is an emerging learning paradigm that computes with high dimensional binary vectors. It is attractive because of its energy efficiency and low latency, especially on emerging hardware -- but HDC suffers from low model accuracy, with little theoretical understanding of what limits its performance. We propose a new theoretical analysis of the limits of HDC via a consideration of what similarity matrices can be "expressed" by binary vectors, and we show how the limits of HDC can be approached using random Fourier features (RFF). We extend our analysis to the more general class of vector symbolic architectures (VSA), which compute with high-dimensional vectors (hypervectors) that are not necessarily binary. We propose a new class of VSAs, finite group VSAs, which surpass the limits of HDC. Using representation theory, we characterize which similarity matrices can be "expressed" by finite group VSA hypervectors, and we show how these VSAs can be constructed. Experimental results show that our RFF method and group VSA can both outperform the state-of-the-art HDC model by up to 7.6% while maintaining hardware efficiency.