Let's ignore computational cost for now, and so consider iterated amplification without distillation, and the initial agent is some particular human. Amplification is also going to be simpler -- it just means letting the agent think twice as long.

For example, $A^{0} (Rohin)$ is a question-answering system that just sends me the question, and returns the answer I give after thinking about it for a day. $A^{t} (Rohin)$ refers to the answers I'd give if I had $2^{t}$ days to think about it.

Rather than talk about "human-level", let's talk about "Issa-level" -- agents need to answer questions as well as you could given a day's time.

Then, $A^{0} (Rohin)$ is super-Issa-level on some tasks (e.g. questions about Berkeley culture) and sub-Issa-level on some tasks (e.g. questions about Wikipedia culture). Why is this? Well, for that example, we have different information. But also, presumably there are differences in what we were good at learning, that would have led to differences even if we had the same information. That's the answer to (2) in this context.

The answer to (3) is that with enough time and effort I could answer questions about Wikipedia culture; it would just take me a lot longer to do so relative to you.

The answer to (1) is "idk, but eventually it's possible". For my specific model, one might hope that $t = 13$ would be an upper bound -- at that point I'd get about as much time to answer the question as you have spent living.

The case with iterated distillation and amplification is basically the same:

1. Idk, but eventually it'll happen. (This does rely on the Factored Cognition hypothesis.)

2. A neural net trained by distillation will probably not replicate our skill on tasks perfectly -- what it becomes good at depends on the architecture, training process, the training data it was given, etc. Perhaps humans are really good at social reasoning because it was strongly selected for by evolution, and we didn't give a correspondingly higher amount of training data for the neural net for these social situations, and so it was subhuman at social reasoning.

3. With enough time / computational budget, the agent can (hopefully) replicate whatever (possibly expensive) explicit chunk of reasoning that underlies human performance (even if it was powered by human intuition). This is the Factored Cognition hypothesis. The addition of the distillation step is an extra confounder, but we hope that it doesn't distort anything too much -- its purpose is to improve speed without affecting anything else (though in practice it will reduce capabilities somewhat).

(I might recommend imagining that the first agent has perfect reasoning ability, except that it is very slow. This means that for any question, the first agent could answer it, given unlimited amounts of time. I wouldn't actually make this claim of IDA, but I think it is instructive for building intuitions.)