Search embeddings with spectral graph awareness

ArrowSpace is spectral vector search that augments nearest-neighbor search with graph Laplacian features. It computes a Laplacian over the item graph and uses the Rayleigh quotient to produce a lambda-tau (λτ) score per item, so retrieval respects both semantic similarity and structural role rather than raw distance alone - higher lambda-tau values indicate items that are both semantically close and structurally central in the graph.

Use it when cosine or L2 similarity misses latent structure in embeddings, when graph-based retrieval with spectral awareness is needed, when characterizing the spectral properties of an embedding space, or when building RAG pipelines where contextual role matters alongside semantic content. Don't use it with fewer than 10 items, since the graph structure isn't meaningful at that scale, and don't use it for real-time streaming data - ArrowSpace is batch-oriented, not designed for real-time indexing. Its own limitations note it does not replace environment-specific validation, testing, or expert review. Two failure modes come up in practice: an eps set too small produces a disconnected graph, fixed by increasing eps or setting it proportional to 1/sqrt(embedding dimension), and a k set too large produces a dense graph with washed-out spectral features, so k is kept at 25 or below for most datasets.

pip install arrowspace

Input is an (N, d) float64 NumPy array of embedding vectors, plus graph parameters (eps, k, topk, p, sigma) passed to an ArrowSpaceBuilder. Output is a per-item lambda-tau score, available as an array indexed by insertion order (aspace.lambdas()) or as ascending (score, index) pairs (aspace.lambdas_sorted()). Worked examples cover basic spectral retrieval over a random embedding set and a direct comparison of the resulting spectral ranking against a cosine-similarity ranking on the same items.

Built on NumPy arrays, it composes naturally with existing embedding pipelines - for example comparing its spectral ranking against scikit-learn's cosine similarity ranking on the same item set. It complements four related skills rather than replacing them: vector-database-engineer for general vector database expertise, embedding-strategies for model selection and chunking, similarity-search-patterns for semantic search implementation, and hybrid-search-implementation for combined semantic and keyword search.

Engineers building RAG or retrieval pipelines who need embeddings ranked by both semantic similarity and structural role in the data - not just raw cosine or L2 distance - and who want tuning guidance (normalize embeddings to unit norm, set eps proportional to 1/sqrt(dimension), keep k between 3 and 25, let sigma auto-select) instead of guessing graph parameters from scratch.