ArrowSpace: Spectral Search for Embeddings and Graph Analysis
The paper describing the ArrowSpace library: a spectral indexing approach for vector similarity search that combines traditional semantic similarity with graph-based spectral properties.
Abstract
arrowspace is a library that implements a novel spectral indexing approach for vector similarity search, combining traditional semantic similarity with graph-based spectral properties. The library introduces taumode (λτ) indexing, which blends Rayleigh-quotient smoothness energy from graph Laplacians with edge-wise dispersion statistics to create bounded, comparable spectral scores. This enables similarity search that considers both semantic content and spectral characteristics of high-dimensional vector datasets.
The bound matters operationally: scores remain comparable across collections, time windows, and model updates, which supports re-ranking and thresholding in production pipelines and gives interpretable rationales for why items rank together.
Contributions
- A spectral indexing scheme combining Rayleigh-quotient smoothness energy from graph Laplacians with edge-wise dispersion statistics.
- Bounded (λτ) scores per item, in [0, 1), enabling calibration across datasets.
- An implementation of the approach in a maintained open-source library.
Reproducibility
- Core library (Rust): tuned-org-uk/arrowspace-rs, Apache-2.0.
- Python bindings: tuned-org-uk/pyarrowspace (
pip install arrowspace). - Worked examples live in the repository’s
examples/directory. - A live industrial setting is the CVE search demo over the NVD corpus.
BibTeX
@article{moriondo2025arrowspace,
title = {ArrowSpace: Spectral Search For Embeddings and Graph Analysis},
author = {Moriondo, Lorenzo},
year = {2025},
doi = {10.21105/joss.09002},
url = {https://doi.org/10.21105/joss.09002}
}