Ajeya has a simple model of future accelerating growth in the post here. Maybe the first doubling of the pace took 12 months. So with twice the pace, maybe the next doubling will take 6 months, then 3 months, then 1.5 months, etc, hitting limits within 12 months.
I think this argument doesn't really work as stated, but that a different argument still ends up supporting the idea that growth will accelerate until it hits extremely high levels.
The problem with the model is that it assumes that the first doubling came entirely from AIs getting more capable in that first year, and that AI's increasing ability to help with AI R&D was enough to not only overcome the diminishing returns from "ideas getting harder to find", but also to double the pace of progress on top of that.
But in fact (if the numbers from the METR assessment are right) what happened in the last year was that the combination of the 'normal' increase in exogenous inputs (e.g.: 3x scale-up of compute per year) and AI's increasing ability to help with AI R&D was enough to double the pace of progress.
This is importantly different, because if this "normal" increase in exogenous input was essential for fully doubling the pace of progress, then we can't extrapolate that the next 6 month period will be enough to double the pace of progress again. Because in the 6 month period, we'll only have half as big of an increase in exogenous inputs (maybe a 1.7x increase in compute rather than the yearly 3x increase).
From very roughly eyeballing the numbers, my current wild guess would be that, over the last year, the following three effects were roughly similarly large.
* The normal decrease in pace of progress from "ideas are getting harder to find".
* The normal increase in pace of progress from exogenous inputs scaling up.
* The novel increase in pace of progress from AI getting good enough to help more with AI R&D.
(At the beginning of the year, there was also a bump in exogenous inputs on top of the no
