SESKStuff Everyone Should Know
SESK: Stuff Everyone Should Know · sesk.info/ai-cosine-ignores-vector-length

What property does cosine similarity ignore when comparing two embeddings?

It ignores vector length and uses their angle.

Start playing free

  1. Their angle
  2. Their dimension count
  3. Their magnitudes ✔

Why: Cosine similarity divides the dot product by both vector lengths. The result depends on direction, unlike a raw dot product, which also grows with magnitude.

Huh, didn't know that: For unit-length vectors, cosine similarity and dot product are equal.

The dad joke
Cosine judged the angle, not the size of the vector's ego.
Like this card?
Play the game

References

Answer: Their magnitudes. Cosine similarity divides the dot product by both vector lengths. The result depends on direction, unlike a raw dot product, which also grows with magnitude.

  1. Google Machine Learning: Measuring similarity from embeddings developers.google.com/machine-learning/clustering/dnn-clustering/supervised-similarity
    In contrast to the cosine, the dot product is proportional to the vector length.
    Checked 2026-10-10.

Think this answer is wrong? Tap "Challenge this answer" on the card in the game and tell us why.

Test yourself in the game

Artificial IntelligenceWhat does a learned embedding assign to each input token?Artificial IntelligenceWhy does a Transformer add positional information to token embeddings?Artificial IntelligenceTo search millions of embeddings fast, what do vector indexes like HNSW usually trade away?

That's stuff everyone should know.