# Hypergraph Embedding Indexing for Efficient Dense Vector Retrieval

arXiv: https://arxiv.org/abs/2608.22980 · HTML: https://mlsanity.com/paper/2608.22980/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [C-Pack: Packed Resources For General Chinese Embeddings](https://mlsanity.com/paper/2309.07597/) (2023)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)

## Abstract (arXiv)

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 activation diversity as a diagnostic metric governing embedding indexability in coordinate-inverted frameworks.