From Embedding Geometry to Spectral Search: Energy Dispersion Networks For Vector Retrieval
The arXiv paper formalising Graph Wiring, Spectral Indexing (SPIN), and tau-modulation for retrieval-augmented pipelines.
Abstract
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.
— arXiv:2606.21535, used under CC BY 4.0.
Contributions
- Graph Wiring: a general framework for exploiting feature-space spectral structure.
- Spectral Indexing (SPIN): the task-specific instantiation for vector search, coupling geometric similarity with spectral information.
- Tau-modulation: adaptive search behaviour for modern RAG pipelines.
- Epiplexity: a theoretical foundation for the approach, and an evaluation across benchmark and industrial settings.
Reproducibility
- Open-source implementation used in the evaluation: arrowspace-rs and pyarrowspace.
- Applied evaluation with protocol and tables: Engineering 001 (CVE and TREC-COVID).
- Industrial deployment: the CVE search demo over the NVD corpus.
BibTeX
@misc{moriondo2026energy,
title = {From Embedding Geometry to Spectral Search: Energy
Dispersion Networks For Vector Retrieval},
author = {Moriondo, Lorenzo and Azizi, Ilias},
year = {2026},
eprint = {2606.21535},
archivePrefix = {arXiv},
primaryClass = {cs.IR},
doi = {10.48550/arXiv.2606.21535},
url = {https://arxiv.org/abs/2606.21535}
}