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I've seen this kind of notion argued in many different contexts, and I don't understand what's the disconnect. Because OF COURSE the LLM has an internal model of the chessboard in the system; that's the only reason it could possibly make moves that are correct at a rate better than chance. That model almost certainly doesn't looks like a model that any human would recognize, such as containing a grid of 8x8 with pieces each representing a team, a position, and a set of allowed moves, which is why it makes mistakes in ways that no human would. But the fact that the model of chess - or the world - would be incomprehensible to humans and isn't based on any real empirical or experienced understanding of physics or rulesets doesn't make it not a model.
I disagree, another possible reason is that simply makes a good (but imperfect) guess as to what's likely to be the next move after a sequence of moves, based on all the chess games stored in its database.
So for example, if the LLM is playing black and you open e4, it's pretty likely that the LLM will respond e5 or c5 for basically the same reason it would likely output "lamb" after "Mary had a little" and "California" after "The Golden Gate bridge is located in"
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