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What Are Vector Embeddings? The Math Behind Semantic Search | Learn in 30 Seconds

"How can I reset my password?" and "Steps to recover your account" share zero keywords — yet they mean the same thing. Keyword search can't connect them. Embeddings can.

An embedding model turns text into a list of numbers — a vector — positioned so that related meanings land near each other. Compare two vectors with cosine similarity or a distance metric, and you get a usable estimate of how related the texts are.

The workflow:
→ Embed your documents
→ Store the vectors in a vector database, alongside document IDs and metadata
→ Embed the incoming question
→ Return the nearest vectors

One detail that breaks real systems: the documents and the query must be encoded by the SAME embedding model. Different models produce different vector spaces, and comparing across them is meaningless — the numbers simply don't line up.

Two honest limits worth knowing:
✘ Proximity is a distance measure, not comprehension — similar sentences don't always land close together
✘ Embeddings retrieve the context; the language model still writes the answer

This is the retrieval half of RAG, which is covered in the previous reel.

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