将向量空间视为谱能量网络，提升检索的语义一致性与灵活性。
From Embedding Geometry to Spectral Search: Energy Dispersion Networks For Vector Retrieval
- 结合几何相似性与谱结构信息进行向量检索
- 在头部尾部一致性与语义对齐上优于纯几何方法
- 支持动态调节搜索行为，适合现代RAG系统
高维向量空间，尤其是具有密集语义结构的嵌入空间，通常仅通过几何关系进行解释。本文提出，这些空间也可被视为由特征空间流形拓扑所诱导的谱能量网络，并带来下游任务的改进。基于此视角，我们引入图连接（Graph Wiring）框架，及其面向向量搜索的任务特化实例——谱索引（Spectral Indexing）。通过融合几何相似性与谱信息，该方法在头部-尾部一致性及语义对齐方面优于纯几何检索方法。此外，其支持通过tau调制实现自适应搜索行为，满足现代检索增强生成（RAG）管道对灵活性的需求。我们完整呈现算法流程，通过极值复杂度（epiplexity）建立理论基础，并在基准与工业场景中使用开源arrowspace库进行评估。
原文摘要 · Abstract (English)
High-dimensional vector spaces, particularly embedding spaces with dense semantic structure, are often interpreted primarily leveraging solely geometric relationships. In this work, we show that they can also be viewed as spectral energy networks induced by the topology of their underlying feature-space manifold with relevant improvements for downstream tasks. Building on this perspective, we introduce Graph Wiring, a general framework for exploiting feature-space spectral structure, together with Spectral Indexing, its task-specific instantiation for vector search. By coupling geometric similarity with spectral information, the proposed method improves Head-Tail coherence and semantic alignment relative to purely geometric retrieval methods. It further supports adaptive search behavior through tau-modulation, providing the flexibility increasingly required by modern Retrieval-Augmented Generation (RAG) pipelines. We present the complete algorithmic pipeline, establish its theoretical foundation through epiplexity, and evaluate the approach across benchmark and industrial settings using the open-source arrowspace library.
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