Cosine ignores length. Dot product rewards it.
Ten Larkspur Cloud handbook chunks drawn as 2D vectors, so you can see the angles. The vectors are hand-placed; every score is computed. Stretch the long pricing page the way an un-normalized model would, and compare the three rankings.
- Top by cosine
- Top by dot product
- Top by Euclidean
- All three rankings agree
Three scores for every chunk
Sorted by cosine; rank under each metric beneath the score
| Chunk | Cosine | Dot | Euclidean | Golden set |
|---|
Higher is closer for cosine and dot; lower is closer for Euclidean distance. A rank in magenta differs from the cosine rank.
The vectors
Dashed circle: length 1. Arrows longer than 2.1 stop at the edge.
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