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Honest questions,

Isn't it very likely chess games were part of the training data? If so, chess sequences seem like an amazing matched filter of sorts. It doesn't seem surprising that it can guess a next move.

Is it teaching itself anything here? Is the model being updated in any way? Or are you talking more generally, looking into the future sort of statement?

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You can put every chess game ever played in its database and yet every time it plays a new game it will immediately come across a completely unique move. So it still needs to learn the rules and know how to play independently. Whether it can do that or not is yet undermined.

I think they meant “teach itself” in the course of a conversation, within the token limit. ChatGPT will forget what it has “learned” once the conversation is over.

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