It doesn't. An LLM uses modeling to approximate the shape of a question and generate a novel answer within the parameters. It's like a shortcut to actually knowing everything and providing authoritative answers.

Sort of like the Scrabble champion who won in Spanish and French despite not knowing those languages. He simply learned patterns of words he could build with letters, but he didn't know the meaning of any of the words.

The holodeck ostensibly has access to all of federation knowledge and history, and when it has to generate novel information (like what would Einstein say to Newton while playing poker) then it extrapolates that informtation based on the sum total of existing information. The holodeck computer has a thorough understanding of the question, the parameters, and the answers (holograms) it creates. It isn't abstracting the question or approximating the shape of the answer.