ArrowSpace

Fast spectral vector search that finds similarity beyond traditional distance metrics

ArrowSpace is a high-performance Rust library for vector similarity search that goes beyond geometric distance (cosine, L2) by incorporating spectral graph properties, enabling more nuanced similarity matching for scientific and structured data.

ArrowSpace is a data structure library that encapsulates the use of λτ indexing; a novel scoring method that mixes Rayleigh and Laplacian scoring (see RESEARCH.md) for building vector-search-friendly lookup tables with built-in spectral-awareness. This allows better managing of datasets where spectral characteristics are most relevant. It pairs dense, row‑major arrays with per‑row spectral scores (λτ) derived from a Rayleigh-Laplacian score built over items, enabling lambda‑aware similarity, range queries, and composable operations like superposition and element‑wise multiplication over rows. It has been designed to work on datasets where spectral characteristics can be leveraged to find matches that are usually ranked lower by commonly used distance metrics.

Run cargo run --example proteins_lookup for an example about how it compares with cosine similarity.

Usage

```rust use arrowspace::builder::ArrowSpaceBuilder;

// Simple example that works immediately let vectors = vec![ vec![1.0, 2.0, 3.0], vec![2.0, 3.0, 1.0], vec![3.0, 1.0, 2.0], ];

let (aspace, _) = ArrowSpaceBuilder::new() .build(vectors); ```

Requirements

• Rust 1.78+ (edition 2024)

Installation

As a Library Dependency

Add to your Cargo.toml: toml [dependencies] arrowspace = "*"

From Source

bash git clone https://github.com/Mec-iS/arrowspace-rs cd arrowspace-rs cargo build --release

Running Examples

bash cargo run --example compare_cosine cargo run --example proteins_lookup

Running Tests

bash cargo test

Run Bench

$ cargo bench

Minimal usage

Construct an ArrowSpace from rows and compute a synthetic index λτ used in similarities search (spectral search):

• Build λτ‑graph from data (preferred path):
  • Use ArrowSpaceBuilder::new().build(items) to get an ArrowSpace and its Laplacian+Tau mode; the builder will compute per‑row synthetic indices immediately.
  • Use ArrowSpaceBuilder::new().with_lambda_graph(...).build(items) to get an ArrowSpace and its Laplacian+Tau mode by specifying the parameters for the graph where the Laplacian is computed.
  • Use ArrowSpaceBuilder::new().with_lambdas(...).with_synthesis(...).build(items) to get an ArrowSpace and its Laplacian+Tau indices by specifying which lambdas values to use.
• Search the space: ```rust use arrowSpace::builder::ArrowSpaceBuilder; use arrowSpace::core::ArrowItem;

// define the search parameters: alpha=1.0 is equivalent to cosine similarity let alpha = 0.7; let beta = 0.3;

// Build ArrowSpace from item vectors let items = vec![ vec![1.0, 2.0, 3.0], // Item 1 vec![2.0, 3.0, 1.0], // Item 2 vec![3.0, 1.0, 2.0], // Item 3 ];

let (aspace, graph) = ArrowSpaceBuilder::new() .withlambdagraph(0.5, 3, 2.0, sigma: 0.25) .build(items);

// prepare query vector let query = aspace.preparequeryitem(vec![1.5, 2.5, 2.0], &graph); // search the space let results = aspace.searchlambdaaware(&query, 1, alpha); println!("{:?}", results);

```

Main Features (spectral graph construction and search)

• Data structure for vector search:
  • Lambda+Tau graph from data (default): builds a Laplacian over items from the row matrix, then computes per‑row synthetic λτ using laplacian + TauMode (see paper) with Median policy by default; override via with_synthesis(alpha, mode) to change α or τ policy.
  • Direct lambda ε‑graph (lower‑level): constructs a Laplacian from a vector of λ values with ε thresholding and k‑capping, union‑symmetrized CSR; use when supplying external λ instead of synthetic.
  • (optional) Hypergraph overlays: build Laplacians from hyperedges (clique expansion, normalized variant) and overlay “boosts” to strengthen pairs; for prebuilt/hypergraph paths, synthetic λ is opt‑in via with_synthesis.
  • (optional) Ensembles: parameterized variants (k adjust, radius/ε expand, hypergraph transforms) for graph experimentation while reusing the same data matrix; synthetic λ is computed per chosen base when enabled.
• Examples:
  • End‑to‑end examples: protein‑like lookup with λ‑band range query using a ZSET‑style index; showcases for hypergraph, λ‑graph, and synthetic laplacian + TauMode flows.
  • Extensive tests spanning ArrowSpace algebra, Rayleigh properties, lambda scale‑invariance, superposition bounds, λ‑graph symmetry and k‑capping semantics, hypergraph correctness, diffusion/random‑walk simulations, fractal integrations, and synthetic λ via Median/Mean/Percentile τ policies.

Key concepts

See paper