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I don't ask how to make it summarize xy but if it is known how a "LLM" understands and performs this meta task at all.

The same is true for prompts like "Be brief" or "Explain in a few sentences". Since this works, the LLM must actually have an understanding of text length.

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Well, you have to think that LMM are just next-token-predictors, so if you let it read a lot of text from the web/textbooks, probably they will learn that after "Be brief" there is a summarization of the text given before, which means to exclude certain words, to phrase stuff in a certain way and so on

You might also be interested in this paper

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