# A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

arXiv: https://arxiv.org/abs/2112.15424 · HTML: https://mlsanity.com/paper/2112.15424/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 446 references that are in the map.
- First posted on arXiv 12 Nov 2021.

## Builds on (most cited first, 30 of 67)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [How to represent part-whole hierarchies in a neural network](https://mlsanity.com/paper/2102.12627/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [Benchmarking TinyML Systems: Challenges and Direction](https://mlsanity.com/paper/2003.04821/) (2020)
- [Superposition of many models into one](https://mlsanity.com/paper/1902.05522/) (2019)
- [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)
- [Associative Long Short-Term Memory](https://mlsanity.com/paper/1602.03032/) (2016)
- [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)
- [Robust High-dimensional Memory-augmented Neural Networks](https://mlsanity.com/paper/2010.01939/) (2020)
- [A theory of sequence indexing and working memory in recurrent neural networks](https://mlsanity.com/paper/1803.00412/) (2018)
- [Attention Approximates Sparse Distributed Memory](https://mlsanity.com/paper/2111.05498/) (2021)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [RNNs Implicitly Implement Tensor Product Representations](https://mlsanity.com/paper/1812.08718/) (2018)
- [Learning with Holographic Reduced Representations](https://mlsanity.com/paper/2109.02157/) (2021)

## Built on by (most cited first, 30 of 69)

- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architectures](https://mlsanity.com/paper/2205.09208/) (2022)
- [Neuromorphic Visual Scene Understanding with Resonator Networks](https://mlsanity.com/paper/2208.12880/) (2022)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [HDC-MiniROCKET: Explicit Time Encoding in Time Series Classification with Hyperdimensional Computing](https://mlsanity.com/paper/2202.08055/) (2022)
- [Unpaired Image Translation via Vector Symbolic Architectures](https://mlsanity.com/paper/2209.02686/) (2022)
- [In-memory factorization of holographic perceptual representations](https://mlsanity.com/paper/2211.05052/) (2022)
- [Hyperdimensional Computing vs. Neural Networks: Comparing Architecture and Learning Process](https://mlsanity.com/paper/2207.12932/) (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)
- [Generalized Holographic Reduced Representations](https://mlsanity.com/paper/2405.09689/) (2024)
- [Hyperdimensional Representation Learning for Node Classification and Link Prediction](https://mlsanity.com/paper/2402.17073/) (2024)
- [Shift-Equivariant Similarity-Preserving Hypervector Representations of Sequences](https://mlsanity.com/paper/2112.15475/) (2021)
- [Unsupervised Dialogue Topic Segmentation in Hyperdimensional Space](https://mlsanity.com/paper/2308.10464/) (2023)
- [Laplace-HDC: Understanding the geometry of binary hyperdimensional computing](https://mlsanity.com/paper/2404.10759/) (2024)
- [Vector-Symbolic Architecture for Event-Based Optical Flow](https://mlsanity.com/paper/2405.08300/) (2024)
- [A Walsh Hadamard Derived Linear Vector Symbolic Architecture](https://mlsanity.com/paper/2410.22669/) (2024)
- [Dynamic Epistemic Friction in Dialogue](https://mlsanity.com/paper/2506.10934/) (2025)
- [Streaming Encoding Algorithms for Scalable Hyperdimensional Computing](https://mlsanity.com/paper/2209.09868/) (2022)
- [Resource-Efficient Federated Hyperdimensional Computing](https://mlsanity.com/paper/2306.01339/) (2023)
- [HDReason: Algorithm-Hardware Codesign for Hyperdimensional Knowledge Graph Reasoning](https://mlsanity.com/paper/2403.05763/) (2024)
- [Compositional Factorization of Visual Scenes with Convolutional Sparse Coding and Resonator Networks](https://mlsanity.com/paper/2404.19126/) (2024)
- [Distributed Representations Enable Robust Multi-Timescale Symbolic Computation in Neuromorphic Hardware](https://mlsanity.com/paper/2405.01305/) (2024)
- [Recursive Binding for Similarity-Preserving Hypervector Representations of Sequences](https://mlsanity.com/paper/2201.11691/) (2022)
- [Generalized Key-Value Memory to Flexibly Adjust Redundancy in Memory-Augmented Networks](https://mlsanity.com/paper/2203.06223/) (2022)
- [Graph Embeddings via Tensor Products and Approximately Orthonormal Codes](https://mlsanity.com/paper/2208.10917/) (2022)
- [The Hyperdimensional Transform: a Holographic Representation of Functions](https://mlsanity.com/paper/2310.16065/) (2023)
- [Decodable and Sample Invariant Continuous Object Encoder](https://mlsanity.com/paper/2311.00187/) (2023)
- [The Hyperdimensional Transform for Distributional Modelling, Regression and Classification](https://mlsanity.com/paper/2311.08150/) (2023)

## Abstract (arXiv)

This is Part II of the two-part comprehensive survey devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations. Holographic Reduced Representations is an influential HDC/VSA model that is well-known in the machine learning domain and often used to refer to the whole family. However, for the sake of consistency, we use HDC/VSA to refer to the field. Part I of this survey covered foundational aspects of the field, such as the historical context leading to the development of HDC/VSA, key elements of any HDC/VSA model, known HDC/VSA models, and the transformation of input data of various types into high-dimensional vectors suitable for HDC/VSA. This second part surveys existing applications, the role of HDC/VSA in cognitive computing and architectures, as well as directions for future work. Most of the applications lie within the Machine Learning/Artificial Intelligence domain, however, we also cover other applications to provide a complete picture. The survey is written to be useful for both newcomers and practitioners.