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

2026-06-19

AI Summary

Traditional vector retrieval relies on pairwise geometric similarity, which struggles to simultaneously achieve semantic alignment and consistency with the head-tail distribution of data. This work proposes a Graph Wiring framework combined with Spectral Indexing, modeling the embedding space as an energy network induced by the topology of feature column vectors. By integrating geometric similarity with spectral structural information and introducing τ-modulation for adaptive retrieval, the method leverages spectral graph theory, energy-based modeling, and epiplexity analysis. Implemented using the open-source arrowspace library, it significantly outperforms purely geometric retrieval across multiple benchmarks and industrial applications, effectively enhancing both semantic alignment and distributional consistency to meet the demands of modern RAG systems for flexible and efficient retrieval.

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.

Problem

• vector retrieval
• spectral graph
• embedding geometry
• semantic alignment
• Retrieval-Augmented Generation

Innovation

• Spectral Indexing
• Graph Wiring
• Energy Dispersion Networks
• tau-modulation
• epiplexity