Why can cosine similarity and dot product rank unnormalized embeddings differently?

Cosine similarity is the dot product divided by the product of the two vector magnitudes. Therefore cosine removes vector-length effects and compares direction, while raw dot product includes both direction and magnitude.

If two vectors are not unit-normalized, a vector with a large norm can receive a high dot-product score even when its direction is not the best match. Cosine can rank that same vector lower because it ignores magnitude.

The trade-off is semantic intent. If vector magnitude carries useful information learned by the model, dot product can be the correct metric. If magnitude is mostly an artifact and direction represents similarity, cosine is usually more appropriate.

In current Qdrant implementations, cosine vectors are normalized for efficient comparison, effectively allowing the distance calculation to use dot product after normalization. Do not infer from that that raw dot-product and cosine are equivalent for arbitrary unnormalized vectors; they are equivalent in ranking only when the vectors are unit-normalized.