If you have e.g. cosine distance as the final layer, if the label is 1 you reward the cosine distance being close to 1, if the label is 0 you reward the cosine distance being close to 0.

The finetuning here is specific to optimizing for retrieval, which may be different than just matching documents, which can be an advantage.

You may want to force the query and document finetunings to be the same, which makes a lot of sense, but the advantage in them differing can be that query strings are often rather short, and in a different sort of language structure than documents, so the differing query and document tunings can in some sense "normalize" queries and documents to be in the same space, when it works well.

This has got me curious. I don't really understand how binary labels could give us embeddings that are well-ordered by distance. For a training pair where (Q, D) are highly similar and a pair where (Q, D) are just barely related, the model is being trained that they're the same distance apart. Is there something I'm not seeing here?

See contrastive losses and siamese networks, like here (where they use L2 distance):

https://lilianweng.github.io/posts/2021-05-31-contrastive/

If documents are similar, you want the two embeddings to be close to each other, if they are dissimilar, you want them to be far apart.

Binary relevance judgements of course don't necessarily produce an ordering, but usually over a large enough set of training examples some will be better matches than others.

"Learning to Rank" gets you into all kinds of labels and losses if you want to go down that rabbit hoel.