Seeing the distribution calibration you point out does update my opinion a bit.
I feel like there’s still a significant distinction though between adding one calculation step to the question versus asking it to model multiple responses. It would have to model its own distribution in a single pass rather than having the distributions measured over multiple passes align (which I’d expect to happen if the fine-tuning teaches it the hypothetical is just like adding a calculation to the end).
As an analogy, suppose I have a pseudorandom black box function that returns an integer. In order to approximate the distribution of its outputs mod 10, I don’t have to know anything about the function; I just can just sample the function and apply mod 10 post hoc. If I want to say something about this distribution without multiple samples, then I actually have to know something about the function.
There is relatedwork you may find interesting. We discuss them briefly in section 5.1 on “Know What They Know”. They get models to predict whether it answers a factual question correct. E.g. Confidence : 54%. In this case, the distribution is only binary (it is either correct or wrong), instead of our paper’s case where it is (sometimes) categorical. But I think training models to verbalize a categorical distribution should work, and there is probably some related work out there.
We didn’t find much related work on whether a model M1 has a very clear advantage in predicting its own distribution versus another model M2 predicting M1. This paper has some mixed but encouraging results.
Seeing the distribution calibration you point out does update my opinion a bit.
I feel like there’s still a significant distinction though between adding one calculation step to the question versus asking it to model multiple responses. It would have to model its own distribution in a single pass rather than having the distributions measured over multiple passes align (which I’d expect to happen if the fine-tuning teaches it the hypothetical is just like adding a calculation to the end).
As an analogy, suppose I have a pseudorandom black box function that returns an integer. In order to approximate the distribution of its outputs mod 10, I don’t have to know anything about the function; I just can just sample the function and apply mod 10 post hoc. If I want to say something about this distribution without multiple samples, then I actually have to know something about the function.
There is related work you may find interesting. We discuss them briefly in section 5.1 on “Know What They Know”. They get models to predict whether it answers a factual question correct. E.g. Confidence : 54%. In this case, the distribution is only binary (it is either correct or wrong), instead of our paper’s case where it is (sometimes) categorical. But I think training models to verbalize a categorical distribution should work, and there is probably some related work out there.
We didn’t find much related work on whether a model M1 has a very clear advantage in predicting its own distribution versus another model M2 predicting M1. This paper has some mixed but encouraging results.
That makes sense. It’s a good suggestion and would be an interesting experiment to run.