Hyperbolic model fits METR capabilities estimate worse than exponential model
This is a response to https://www.lesswrong.com/posts/mXa66dPR8hmHgndP5/hyperbolic-trend-with-upcoming-singularity-fits-metr which claims that a hyperbolic model, complete with an actual singularity in the near future, is a better fit for the METR time-horizon data than a simple exponential model. I think that post has a serious error in it and its conclusions are the reverse of correct. Hence this one. (An important remark: although I think Valentin2026 made an important mistake that invalidates his conclusions, I think he did an excellent thing in (1) considering an alternative model, (2) testing it, (3) showing all his working, and (4) writing it up clearly enough that others could check his work. Please do not take any part of this post as saying that Valentin2026 is bad or stupid or any nonsense like that. Anyone can make a mistake; I have made plenty of equally bad ones myself.) [EDITED to add:] Valentin2026 has now (5) agreed that the thing I think was an error was an error, and (6) edited his post to say so. Thanks, Valentin! The models Valentin2026's post compares the results of fitting two different models to METR's time-horizon benchmark data (METR's original blogpost is at https://metr.org/blog/2025-03-19-measuring-ai-ability-to-complete-long-tasks/ but the data have been updated since then, most recently as of current writing to account for the GPT-5 launch). One model, or more accurately one family of models, is hyperbolic: if we let H be the time horizon estimate produced by METR, the model is H=A/(t1−t)q where t1 is the time at which the estimate shoots off to infinity ("the singularity", though note that divergence here does not necessarily imply e.g. superintelligence in any very strong sense), A is an overall scale factor, and q is larger when the divergence happens more abruptly. (If you start with a Moore's-law sort of model of technological progress dHdt=kH and then suppose that actually progress gets faster in proportion to H, dHdt=kH2,
So far as I can tell, the most plausible way for the universe to be deterministic is something along the lines of "many worlds" where Reality is a vast superposition of what-look-to-us-like-realities, and if the future of AI is determined what that means is more like "15% of the future has AI destroying all human value, 10% has AI ushering in a utopia for humans, 20% has it producing a mundane dystopia where all the power and wealth is in a few not-very-benevolent hands, 20% has it improving the world in mundane ways, and 35% has it fizzling out and never making much more change than it already has done" than like "it's already determined that AI will/won't kill us all".
(For the avoidance of doubt, those percentages are not serious attempts at estimating the probabilities. Maybe some of them are more like 0.01% or 99.99%.)