arrowspace

ArrowSpace

Spectral vector search that augments nearest-neighbour search with graph Laplacian features. Computes a Laplacian over the item graph and uses the Rayleigh quotient to produce a λτ (lambda-tau) score per item, enabling search that respects both semantic similarity and structural role.

When to Use This Skill

• Cosine or L2 similarity misses latent structure in your embeddings
• You want graph-based retrieval with spectral awareness
• You need to characterise the spectral properties of an embedding space
• You are building RAG pipelines where contextual role matters alongside semantic content

How It Works

Step 1: Install and import

pip install arrowspace

from arrowspace import ArrowSpaceBuilder
import numpy as np

Step 2: Prepare your data

Pass an (N, d) float64 NumPy array of embedding vectors:

items = np.array([[0.1, 0.2, 0.3],
                  [0.0, 0.5, 0.1],
                  [0.9, 0.1, 0.0]], dtype=np.float64)

Step 3: Configure graph parameters

graph_params = {"eps": 0.2, "k": 6, "topk": 3, "p": 2.0, "sigma": 1.0}
builder = ArrowSpaceBuilder(items, graph_params=graph_params)
aspace = builder.build()

Step 4: Query

lambdas = aspace.lambdas()           # array indexed by insertion order
sorted_res = aspace.lambdas_sorted()  # (score, index) pairs ascending

Hig