Not sure if I’m misunderstanding this, but it seems to me that if it takes 10,000 bits to specify the intended head and 1000 bits to specify the instrumental head, that’s because the world model—which we’re assuming is accurate—considers humans that answer a question with a truthful and correct description of reality much rarer than humans who don’t.
I don’t think the complexity of the head is equal to frequency in the world model. Also I’m not committed to the simplicity prior being a good prior (all I know is that it allowed the AI to learn something the human didn’t understand). And most importantly, a human who answers honestly is not the same as the model’s honest answer—they come apart whenever the human is mistaken.
So if I understand correctly, the right amount of bits saved here would be 9,000.
I think 10,000 is right? 2^{-10,000} of all possible functions answer questions correctly. 2^{-1,000} of possible functions look up what the human says, but that’s not relevant for computing P(the human answers questions correctly). (I assume you were computing 9,000 as 10,000 − 1,000.)
I don’t think the complexity of the head is equal to frequency in the world model. Also I’m not committed to the simplicity prior being a good prior (all I know is that it allowed the AI to learn something the human didn’t understand). And most importantly, a human who answers honestly is not the same as the model’s honest answer—they come apart whenever the human is mistaken.
I think 10,000 is right? 2^{-10,000} of all possible functions answer questions correctly. 2^{-1,000} of possible functions look up what the human says, but that’s not relevant for computing P(the human answers questions correctly). (I assume you were computing 9,000 as 10,000 − 1,000.)