# HyperSpace: A Generalized Framework for Spatial Encoding in Hyperdimensional Representations

arXiv: https://arxiv.org/abs/2604.15113 · HTML: https://mlsanity.com/paper/2604.15113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 16 Apr 2026.

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

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Converting Static Image Datasets to Spiking Neuromorphic Datasets Using Saccades](https://mlsanity.com/paper/1507.07629/) (2015)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [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)
- [HEAL: Brain-inspired Hyperdimensional Efficient Active Learning](https://mlsanity.com/paper/2402.11223/) (2024)
- [Brain Inspired Probabilistic Occupancy Grid Mapping with Vector Symbolic Architectures](https://mlsanity.com/paper/2408.09066/) (2024)
- [Generalizable Reinforcement Learning with Biologically Inspired Hyperdimensional Occupancy Grid Maps for Exploration and Goal-Directed Path Planning](https://mlsanity.com/paper/2502.09393/) (2025)

## Abstract (arXiv)

Vector Symbolic Architectures (VSAs) provide a well-defined algebraic framework for compositional representations in hyperdimensional spaces. We introduce HyperSpace, an open-source framework that decomposes VSA systems into modular operators for encoding, binding, bundling, similarity, cleanup, and regression. Using HyperSpace, we analyze and benchmark two representative VSA backends: Holographic Reduced Representations (HRR) and Fourier Holographic Reduced Representations (FHRR). Although FHRR provides lower theoretical complexity for individual operations, HyperSpaces modularity reveals that similarity and cleanup dominate runtime in spatial domains. As a result, HRR and FHRR exhibit comparable end-to-end performance. Differences in memory footprint introduce additional deployment trade-offs where HRR requires approximately half the memory of FHRR vectors. By enabling modular, system-level evaluation, HyperSpace reveals practical trade-offs in VSA pipelines that are not apparent from theoretical or operator-level comparisons alone.