From Embedding Geometry to Spectral Search: Energy Dispersion Networks For Vector Retrieval

• URL: http://arxiv.org/abs/2606.21535v1
• Date: Fri, 19 Jun 2026 15:33:35 GMT
• Title: From Embedding Geometry to Spectral Search: Energy Dispersion Networks For Vector Retrieval
• Abstract summary: We introduce Graph Wiring, a framework for exploiting feature-space spectral structure, together with Spectral Indexing.<n>By coupling geometric similarity with spectral information, the proposed method improves head-tail coherence and semantic alignment.<n>We present the complete algorithmic pipeline, establish its theoretical foundation through epiplexity, and evaluate the approach across benchmark and industrial settings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Vector spaces, such as embedding spaces that encode dense semantic information, need not be analyzed solely through pointwise geometry. They can also be interpreted as energy networks through the spectral graph induced by the topology of their column vectors, i.e., their feature-space structure. 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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