HyperSpace: A Generalized Framework for Spatial Encoding in Hyperdimensional Representations

TL;DR

HyperSpace is an open-source framework that modularly analyzes and benchmarks vector symbolic architectures, revealing practical performance and memory trade-offs between HRR and FHRR in hyperdimensional spaces.

Contribution

HyperSpace introduces a modular framework for analyzing VSAs, enabling system-level evaluation of different backends like HRR and FHRR.

Findings

FHRR has lower theoretical complexity but similar end-to-end performance to HRR.

Memory footprint of HRR is about half that of FHRR.

Modularity reveals practical trade-offs not seen in operator-level analysis.

Abstract

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.