(Apologies for the long comment).
I want to make a point about your arguments about the growth of time horizons being superexponential. I think they are generally correct, but I think they need to be downweighted somewhat in the timeline model.
This is how I understand your model:
Our starting point is to take the METR graph and extrapolate it exponentially, as they do, making a guess about what agentic coding time horizon would correspond to the AC milestone.
And then you include adjustments to this extrapolation, some of which are arguments about superexponential growth that don’t have anything to do with AI R&D speedups feeding back into themselves. Because you are using a threshold on the METR graph to determine when ACs happen, these arguments about superexponential growth meaningfully affects your prediction of time to ACs.
I consider the casual network to look something like this:
(The METR time horizon level and the level of AI R&D speedup are both driven by the level of effective compute.)
Since we only truly care about AI R&D speedup, we must differentiate between arguments about how fast effective compute will advance or how these advances affect the R&D speedup (which both affect AI R&D speedup and the time to ACs), and arguments about how much effective compute will affect the METR time horizon (which is not what we ultimately care about).
The argument that superexponential growth is implied by infinite time horizons is purely an argument about the relationship between effective compute and the METR time horizon. Whether or not it is true does not change the level of effective compute you need to get ACs. This also applies to your second argument for superexponential growth (that doublings get easier to achieve naturally because less effective compute is needed to jump from 1 month to 4 months than from 1 week to 4 weeks, for example). Again this is only an argument about how increases in effective compute affect the METR time horizon graph, not how fast effective compute is increasing or how increases in effective compute increase AI R&D speedup.
Now this doesn’t mean you have to throw out this entire section of the model. Importantly, it seems like there should be at least some correlation between the relationship between effective compute and the METR time horizon and the relationship between effective compute and the AI R&D speedup. But unless this correlation is 1-1, arguments about superexponential growth that come from the relationship between effective compute and the METR time horizon should be downweighted.
Here’s a toy model to illustrate this better:
Imagine there are four effective compute levels: X1, X2, X3, and X4. X1 is where we are at right now. Let’s say that if METR is exponential in relation to effective compute, we hit Y horizon length at effective compute level X4. On the other hand, if METR is superexponential in relation to effective compute, we hit Y horizon length at capability level X2. Let’s imagine that we thought we would get ACs at effective compute level X4, around where METR was supposed to hit horizon length Y if it were exponential. Suppose we now know that the METR graph is superexponential and will hit Y at X2. How should that affect our expectation of when we will hit ACs? If the correlation between the relationship of effective compute to the METR time horizon and the relationship of effective compute to AI R&D speedup is 1-1, we should update to X2. If there is no correlation, we should keep our estimation at X4. If there is some correlation, maybe we say X3?
The consequences of this are, I think, slightly longer timelines from the model.
Thanks for the reply!
It is a very confusing point and I didn’t explain it well, sorry. I also might just be fundamentally confused and wrong. Hopefully this comment can explain it well enough so you can either shoot it down as incorrect or accept it.
First of all, it might be easier to understand if we replace “effective compute” with “general capabilities” in my original comment. Effective compute causally affects capabilities which causally affects both the METR time horizon measurement and the AI R&D speedup variable. So we can screen off the effective compute node and replace it with a general capabilities node.
I mostly agree with this. However, I think a model having very high time horizons is direct evidence for capabilities being high, which is then direct evidence for AI R&D speedup being high (and thus more likely to be past the AC threshold).
This leads to an important distinction. If you want to argue that AI R&D speedup will be higher (or certain thresholds of AI R&D speedup like AC being reached faster) using the METR graph, your argument fundamentally has to be an argument about capabilities being higher (arriving sooner) or an argument about the relationship between capabilities and AI R&D speedup.
I don’t think that your first argument about the superexponential nature of the METR graph (that infinite time horizons in finite time implies it must be superexponential) is either of these. It seems to be an argument purely about the relationship between capabilities and the METR graph.
I also think your second argument for superexponential growth (that subsequent doublings should get easier because they require less new capabilities than earlier doublings) is mostly an argument about the relationship between capabilities and the METR graph. Although I could maybe see it being an argument about the relationship between capabilities and AI R&D speedup (the last few capabilities to be unlocked provide huge boosts to AI R&D speedup?).
Basically, my core concern is if neither of these arguments are truly arguments about capabilities arriving faster, or about the relationship between capabilities and AI R&D speedup, then why are they being used to update the estimation of time to ACs?
In contrast, arguments about AI R&D feeding back into itself, or about compute investment slowing down, are arguments directly about how fast capabilities will advance. So these validly affect your estimation of time to ACs.
If you disagree with me and think that the arguments for superexponential growth are not just arguments about the relationship between capabilities and the METR graph, then we can focus our discussion there. To the extent that these are also arguments about the things we truly care about, you should adjust time to ACs based on them; this is what I was trying to capture with the correlation stuff in my first comment.
If you do end up agreeing, I also don’t really know how to incorporate this into the model. It seems hard and messy. I think that it is true that using the METR graph is the best thing we can do right now. I just don’t think that these arguments about the superexponential nature of the METR graph should affect the estimation of time to ACs. But I do think that it is superexponential...and I think that it is the best way to estimate time to ACs...so again, messy :(. Hope this makes more sense!