# Embeddings and cosine similarity

> Turn text into a vector so “similar meaning” becomes “small angle”.

Concept · Embeddings & retrieval · https://levelcode.org/concepts/embedding-similarity

An **embedding model** turns a piece of text into a fixed-length vector of numbers, typically 256–3,072 of them. It's trained so that texts with similar meaning end up pointing in similar directions, even when they share no words:

```text
"How do I reset my password?"    → [ 0.12, -0.48,  0.33, … ]
"I forgot my login credentials"  → [ 0.10, -0.45,  0.36, … ]   ← close
"Best pizza in Naples"           → [-0.51,  0.22, -0.07, … ]   ← far
```

## Measuring closeness

**Cosine similarity** is the cosine of the angle between two vectors: 1 means the same direction, 0 unrelated, −1 opposite.

```python
import numpy as np

def cosine(a, b):
    return float(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b)))
```

Many embedding models return **normalized** vectors (length 1). Then cosine similarity equals the plain **dot product**, which is cheaper, and ranking by Euclidean distance gives the same order. Use whichever metric your model's documentation recommends, and configure your vector index to match.

Scores are only meaningful **relative to each other, within one model.** A cosine of 0.8 might be a strong match for one model and a weak one for another. Don't hard-code thresholds without testing them on your own data.

## What embeddings are good for

- **Semantic search:** find documents that answer a question phrased differently. This is the retrieval half of [RAG](https://levelcode.org/roadmaps/ai-engineer/rag).
- **Deduplication and clustering:** group near-identical tickets or reviews.
- **Classification and routing:** compare an input with labelled examples and pick the nearest.
- **Recommendations:** find items similar to ones a user liked.

## Limits

- **Exact terms.** Product codes, error IDs and names often match poorly. Combine embeddings with keyword search ([hybrid search](https://levelcode.org/concepts/hybrid-search-reranking)).
- **Similar isn't the same as relevant.** "How to cancel" and "how not to cancel" embed close together. Reranking helps.
- **Vectors from different models, or different versions of one model, aren't comparable.** Changing models means re-embedding everything.
- **Long inputs get blurred** into one vector. That's why documents are split up first ([chunking](https://levelcode.org/concepts/chunking)).

Comparing a query with millions of vectors one by one is slow, so production systems use [approximate nearest-neighbour indexes](https://levelcode.org/concepts/ann-indexes).