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It is up for testing, but you likely get the effect of "don't think about a pink elephant." So I guess that for most embedding models, "articles about San Francisco that don't mention cars" are closest to articles about SF that mention cars.

The fundamental issue here is comparing apples to oranges, questions, and answers.

So is LLM pre/post-processing the best approach here?

I think you have to separate it into negative query and run (negative) rank and combine results yourself.

no this wont work. embedding models at the moment are pretty bad with negations