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I asked one question, "How do I stop one user from sending too many requests?", and scored one short text about against it. Same model, same two texts. One score came out as 0.741. The other came out as 521.380.

A real screenshot of VS Code's terminal after running python three_ways.py. With the new endpoint /api/embed, every vector has length 1.00 and the rate-limiting text scores cosine 0.741, dot 0.741, distance 0.719. With the old endpoint /api/embeddings, the question's vector has length 26.60, and the rate-limiting text scores cosine 0.741, dot 521.380, distance 19.071.

Neither number is wrong. They come from two different ways of comparing , used on vectors of two different lengths. Both words, vector and length, are explained on the next slide. This lesson is about which way to compare, and the one check that tells you whether the choice matters.

A flat illustration of an engineer at a desk holding a clear protractor over two paper arrows, one short and one long, both pointing in almost the same direction, with a tape measure lying unused beside them. A line asks: two arrows can point the same way and still be different lengths; which one do you measure?

The two paper arrows point almost the same way, but one is much longer. A protractor reads direction, a tape measure reads size, and this lesson is about which of the two to use.

Two panels on the same question, the same text and the same model. Cosine: 0.741, from both endpoints. Dot product on the old endpoint /api/embeddings: 521.380. A note says this is the rate-limiting text scored against one question.

Both panels score the same pair with the same model: my rate-limiting text against one question. Cosine gives 0.741 from both endpoints, and a dot product on the old endpoint gives 521.380.

Cosine, Dot Product or Distance: Which One Compares Embeddings?

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One Pair, Two Very Different Scores