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I think it's more explicit than that, part of post-training to enforce the kind of behavior, I don't think it's emergent but rather researchers steering it to do that because they saw the CoT gets slightly better if the model tries to doubt itself or cheer itself on. Don't recall if there was a paper outlining this, tried finding where I got this from but searches/LLMing turns up nothing so far.
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My understanding is that it’s the result of these companies making sure to keep you engaged/happy less than the result of data these companies train with.

I don’t know if it’s true or not but it certainly tracks given LLMs are way more polite than the average post on the internet lol

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