Cosine similarity vs Euclidean distance in embedding space?

Cosine similarity vs Euclidean distance in embedding space?medium

Type: conceptual
Topic: cosine-similarity-vs-euclidean-distance-in-embedding-space
Frequency: common
Tags: rag, cosine, similarity, euclidean, distance, embedding

Answer

Cosine measures the angle between vectors — magnitude-invariant, preferred for text embeddings where document length varies.

Explanation

Cosine measures the angle between vectors — magnitude-invariant, preferred for text embeddings where document length varies. Euclidean measures absolute distance — sensitive to magnitude. In practice: cosine for semantic similarity (RAG, ranking), Euclidean/L2 for spatial tasks. FAISS supports both via IndexFlatIP (inner product ≈ cosine on normalized vectors) and IndexFlatL2.

Follow-upWhen would you choose one approach over the other?