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This research introduces the Hypergraph Embedding Index (HEI), a novel framework that restructures dense vector retrieval by organizing documents based on combinations of activated latent dimensions rather than treating embeddings as indivisible points. By leveraging multiple complementary hypergraphs, the method significantly improves retrieval coverage and efficiency without incurring the combinatorial costs typically associated with higher dimensionality. The work also establishes "activation diversity" as a critical metric for diagnosing indexability in coordinate-inverted frameworks, offering a fresh perspective on optimizing semantic search infrastructure.
Hypergraph Embedding Indexing for Efficient Dense Vector Retrieval
arXiv:2608.22980v1 Announce Type: cross Abstract: Dense vector retrieval has become the foundation of modern semantic search, yet existing approximate nearest neighbor (ANN) indexes treat an embedding as an indivisible point in a high-dimensional space. In this work, we propose the Hypergraph Embedding Index (HEI), a framework that instead organizes documents according to combinations of highly activated latent embedding dimensions. This formulation enables inverted-index style candidate generation while preserving the semantic ranking capabilities of dense embeddings. We further demonstrate that constructing multiple complementary hypergraphs substantially improves retrieval coverage without the combinatorial growth associated with increasing the dimensionality of a single hypergraph. Finally, we establish that the statistical properties of embedding activations strongly influence coordinate-inverted indexing efficiency, introducing \emph{activation diversity} as a diagnostic metric governing embedding indexability in coordinate-inverted frameworks.
Abstract:Dense vector retrieval has become the foundation of modern semantic search, yet existing approximate nearest neighbor (ANN) indexes treat an embedding as an indivisible point in a high-dimensional space. In this work, we propose the Hypergraph Embedding Index (HEI), a framework that instead organizes documents according to combinations of highly activated latent embedding dimensions. This formulation enables inverted-index style candidate generation while preserving the semantic ranking capabilities of dense embeddings. We further demonstrate that constructing multiple complementary hypergraphs substantially improves retrieval coverage without the combinatorial growth associated with increasing the dimensionality of a single hypergraph. Finally, we establish that the statistical properties of embedding activations strongly influence coordinate-inverted indexing efficiency, introducing \emph{activation diversity} as a diagnostic metric governing embedding indexability in coordinate-inverted frameworks.
Information Retrieval (cs.IR); Artificial Intelligence (cs.AI)
arXiv:2608.22980 [cs.IR]
(or arXiv:2608.22980v1 [cs.IR] for this version)
https://doi.org/10.48550/arXiv.2608.22980 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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