用超图结构组织嵌入维度组合，提升密集向量检索效率
Hypergraph Embedding Indexing for Efficient Dense Vector Retrieval
- 将嵌入向量按激活维度组合建模为超图，实现类似倒排索引的候选生成
- 多互补超图设计显著提升召回覆盖，且不随维度爆炸增长
- 提出激活多样性指标，可评估嵌入在坐标倒排框架下的索引性能
密集向量检索已成为现代语义搜索的基础，但现有近似最近邻（ANN）索引将嵌入视为高维空间中的不可分割点。本文提出超图嵌入索引（HEI）框架，通过组合高度激活的潜在嵌入维度来组织文档。该方法实现了类似倒排索引的候选生成，同时保留了密集嵌入的语义排序能力。进一步表明，构建多个互补超图可显著提升检索覆盖率，且不会伴随单个超图维度增加带来的组合爆炸。最后，我们发现嵌入激活的统计特性强烈影响坐标倒排索引效率，提出‘激活多样性’作为衡量嵌入在坐标倒排框架下可索引性的诊断指标。
原文摘要 · Abstract (English)
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.
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