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However, consider LLM's and the way they actually work. If I want it to create a unique LLM, is it intelligent enough to come up with one that it is not trained with? Does it have enough understanding to compare all the other ones it is trained with and come up with a new one using some probabilistic randomness?

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I would assume it could come up with one it isn't trained with, but a correct, much less novel, result would be due to random chance, not an intelligent awareness of what a sudoku is, and what sudokus already exist.

It might just as well copy half of a New York times sudoku, or make up entirely nonexistent words. As far as I know LLMs can't actually do the math necessary to generate a correct sudoku. It would just give you some "sudoku-like" text.

I'm not an expert on LLMs but based on what I do know, that's what would happen.

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