Better vector search with graphs and spectral indexing (www.tuned.org.uk)

arrowspace has redesigned how it builds and queries graph structure for vector search, targeting datasets up to 100k items and 1k features. The core change reworks Laplacian computation to make graph-based nearest‑neighbor search both cheaper and more consistent: data are condensed through clustering plus density‑aware sampling, feature projection is done proportionally to problem scale using centroids, and the resulting graph is sparsified with a fast spectral method that preserves spectral structure while drastically cutting cost. For practitioners this means more scalable, lower‑latency graph indices with better fidelity to the original geometry. Density‑aware sampling reduces redundancy in dense regions, centroid‑proportional projection limits dimensionality while ensuring queries use the same projection space, and spectral sparsification maintains key Laplacian properties so connectivity and diffusion-based metrics remain accurate. The net implication is a smaller, faster index that retains search quality—beneficial for ANN workflows, semantic search, and any pipeline relying on graph Laplacians for propagation or clustering—without requiring full‑dimensional graphs or expensive all‑pairs computations.