# Recursive Binding for Similarity-Preserving Hypervector Representations of Sequences

arXiv: https://arxiv.org/abs/2201.11691 · HTML: https://mlsanity.com/paper/2201.11691/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 27 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [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)
- [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)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [Learning with Holographic Reduced Representations](https://mlsanity.com/paper/2109.02157/) (2021)
- [Representing Objects, Relations, and Sequences](https://mlsanity.com/paper/1501.07627/) (2015)
- [Neural Distributed Autoassociative Memories: A Survey](https://mlsanity.com/paper/1709.00848/) (2017)
- [Generalized Learning Vector Quantization for Classification in Randomized Neural Networks and Hyperdimensional Computing](https://mlsanity.com/paper/2106.09821/) (2021)
- [Holographic Graph Neuron: a Bio-Inspired Architecture for Pattern Processing](https://mlsanity.com/paper/1501.03784/) (2015)
- [Shift-Equivariant Similarity-Preserving Hypervector Representations of Sequences](https://mlsanity.com/paper/2112.15475/) (2021)

## Built on by (most cited first, 2 of 2)

- [Hyperdimensional Vector Tsetlin Machines with Applications to Sequence Learning and Generation](https://mlsanity.com/paper/2408.16620/) (2024)
- [Real-Valued Hyperdimensional Sequence Representations with Hadamard Product Binding and Shift Equivariance](https://mlsanity.com/paper/2608.28334/) (2026)

## Abstract (arXiv)

Hyperdimensional computing (HDC), also known as vector symbolic architectures (VSA), is a computing framework used within artificial intelligence and cognitive computing that operates with distributed vector representations of large fixed dimensionality. A critical step for designing the HDC/VSA solutions is to obtain such representations from the input data. Here, we focus on sequences and propose their transformation to distributed representations that both preserve the similarity of identical sequence elements at nearby positions and are equivariant to the sequence shift. These properties are enabled by forming representations of sequence positions using recursive binding and superposition operations. The proposed transformation was experimentally investigated with symbolic strings used for modeling human perception of word similarity. The obtained results are on a par with more sophisticated approaches from the literature. The proposed transformation was designed for the HDC/VSA model known as Fourier Holographic Reduced Representations. However, it can be adapted to some other HDC/VSA models.