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mediumAI Engineering

How does similarity search work — cosine, dot product and Euclidean?

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01

Understand the problem

The metrics behind nearest-neighbour retrieval and why ANN indexes make it fast.

similaritycosineannhnsw
02

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Nudge consolestandby

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03

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Similarity search finds the vectors closest to a query vector. Cosine similarity compares direction (angle) ignoring magnitude and is the default for normalized text embeddings; dot product equals cosine when vectors are unit-normalized; Euclidean measures straight-line distance. Exact search is O(n), so vector stores

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04

Read the code

pgvector: metric operators and an HNSW index
-- cosine distance operator: <=>   (dot: <#>, euclidean: <->)
CREATE INDEX ON chunks USING hnsw (embedding vector_cosine_ops);

SELECT id, title, 1 - (embedding <=> $1) AS similarity
FROM chunks
WHERE tenant_id = $2            -- filter + ANN together
ORDER BY embedding <=> $1
LIMIT 10;
05

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