Instead of sums of multiplications you could for example use sum of squares of d... | Hacker News

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		scotty79 on March 12, 2024 \| parent \| context \| favorite \| on: Is Cosine-Similarity of Embeddings Really About Si... Instead of sums of multiplications you could for example use sum of squares of differences. Means squared error instead of dot product, it's not cheaper but it's close If you want to go cheaper you could use sum of abs of differences.

soarerz on March 13, 2024 [–]

This is effectively "the same" as dot product.

For a lot of embeddings we have today, norm of any embedding vector is roughly of same size, so the angle between two vectors is roughly same size as length of difference that you are saying, and can be expressed in terms of 1 - dot product after scaling

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