What are embeddings, and how is semantic similarity computed?

Intuition: "How do I reset my password?" and "I forgot my login credentials" share almost no words but produce nearby vectors. Keyword search would miss the match; embeddings catch it.

How embedding models are trained: usually with contrastive learning. Pairs of related texts (question/answer, title/body) are pulled together, and unrelated texts are pushed apart. Examples: OpenAI text-embedding-3, Cohere Embed, Voyage, Google Gemini embeddings, and open models such as BGE, E5, GTE, Nomic and Jina.

Similarity metrics

• Cosine similarity = (A · B) / (‖A‖ ‖B‖). Ranges from −1 to 1 and ignores vector length.
• Dot product = A · B. Fast. Equals cosine if vectors are L2-normalised (most embedding APIs return normalised vectors).
• Euclidean (L2) distance. For normalised vectors, ranking by L2 equals ranking by cosine.

Use whatever metric the embedding model was trained with, which is usually documented.

Important properties

• Asymmetric retrieval: queries are short, documents long. Many models use different prefixes or modes for "query" and "document" (e.g. E5's query: / passage:). Forgetting this measurably hurts retrieval.
• Max input length: text beyond the model's token limit is truncated silently. Another reason to chunk.
• Vectors from different models are not comparable. Changing the model means re-embedding everything (Q45).

Common mistakes

• Saying "embeddings understand meaning perfectly." They struggle with negation ("not refundable"), exact identifiers (SKU-4471), numbers and rare jargon. This is why hybrid search exists (Q7).

Related

• Previous: Q2. Walk through the two phases of a RAG pipeline: indexing and querying.
• Next: Q4. Why do we chunk documents, and what are the common chunking strategies?
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