HyperSpace: A Generalized Framework for Spatial Encoding in Hyperdimensional Representations

2026-04-16

AI Summary

This work addresses the lack of systematic evaluation of Vector Symbolic Architectures (VSAs) in spatial encoding tasks, particularly regarding component-wise performance and deployment trade-offs. The authors propose HyperSpace, a modular framework that decomposes VSA operations into distinct operators—encoding, binding, bundling, similarity computation, cleanup, and regression—enabling unified benchmarking and system-level analysis across different VSA backends, such as Holographic Reduced Representations (HRR) and Fourier Holographic Reduced Representations (FHRR). Using HyperSpace, the study reveals for the first time that similarity computation and cleanup dominate runtime overhead. Furthermore, while HRR and FHRR exhibit comparable end-to-end performance, HRR requires only half the memory of FHRR, highlighting a significant discrepancy between theoretical complexity and real-world system behavior.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

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.

Problem

• Vector Symbolic Architectures
• Spatial Encoding
• Hyperdimensional Computing
• Performance Trade-offs
• Modular Evaluation

Innovation

• HyperSpace
• Vector Symbolic Architectures
• modular framework
• spatial encoding
• hyperdimensional computing