nearest neighbor search embeddings

Nearest neighbor search over embeddings means: given a query vector, find the most similar vectors in a database of vectors.

Core idea

1. Convert items into embeddings (dense vectors).
2. Store those vectors in an index.
3. For a query embedding, compute similarity to all or many vectors.
4. Return the top-k nearest ones.

Common similarity metrics

• Cosine similarity: compares angle; common for text embeddings.
• Dot product: often used when vectors are normalized.
• Euclidean distance (L2): geometric distance.

If embeddings are normalized, cosine similarity and dot product are closely related.

Exact vs approximate search

Exact nearest neighbor

• Compares against every vector.
• Simple but slow for large datasets.

Approximate nearest neighbor (ANN)

• Trades a tiny bit of accuracy for huge speed gains.
• Used for large-scale search systems.

Common ANN methods:

• HNSW: graph-based, very popular.
• FAISS: library with many indexing options.
• Annoy: tree-based, good for read-heavy workloads.
• ScaNN: optimized for similarity search.

Typical workflow

1. Embed documents/items.
2. Normalize vectors if using cosine similarity.
3. Build an ANN index.
4. Embed the query.
5. Search top-k nearest vectors.
6. Optionally rerank results with a more precise model.

Python example with FAISS

import faiss
import numpy as np

# Example embeddings: 1000 vectors of dimension 128
xb = np.random.rand(1000, 128).astype('float32')
xq = np.random.rand(1, 128).astype('float32')

# If using cosine similarity, normalize vectors first
faiss.normalize_L2(xb)
faiss.normalize_L2(xq)

index = faiss.IndexFlatIP(128)  # inner product for cosine on normalized vectors
index.add(xb)

k = 5
scores, ids = index.search(xq, k)
print(ids)
print(scores)

When to use it

• Semantic search
• Recommendation systems
• Duplicate detection
• Retrieval-Augmented Generation (RAG)
• Clustering / similarity lookup

If you want, I can also show:

• how to do this in Python with scikit-learn / FAISS / Annoy
• how cosine similarity works mathematically
• how to choose the best ANN index for your dataset