That assumption is still there because your interpretation is both not true and not justified by this analysis. As I've noted several times before, time-travel comparisons like this are useful for forecasting, but are not causal models of research: they cannot tell you the consequence of halting compute growth, because compute causes algorithmic progress. Algorithmic progress does not drop out of the sky by the tick-tock of a clock, it is the fruits of spending a lot of compute on a lot of experiments and trial-and-error and serendipity.

Unless you believe that it is possible to create that algorithmic progress in a void of pure abstract thought with no dirty trial-and-error of the sort which actually creates breakthroughs like Resnets or GPTs, then any breakdown like this relying on 'compute used in a single run' or 'compute used in the benchmark instance' simply represents a lower bound on the total compute spent to achieve that progress.

Once compute stagnates, so too will 'algorithmic' progress, because 'algorithmic' is just 'compute' in a trenchcoat. Only once the compute shows up, then the overflowing abundance of ideas will be able to be validated and show which one was a good algorithm after all; otherwise, it's just Schmidhubering into a void and a Trivia Pursuit game like 'oh, did you know resnets and Densenets were first invented in 1989 and they had shortcut connections well before that? too bad they couldn't make any use of it then, what a pity'.

even a pause which completely stops all new training runs beyond current size indefinitely would only ~double timelines at best, and probably less

I'd emphasize that we currently don't have a very clear sense of how algorithmic improvement happens, and it is likely mediated to some extent by large experiments, so I think is more likely to slow timelines more than this implies.

I think this question is interesting but difficult to answer based on the data we have, because the dataset is so poor when it comes to unusual examples that would really allow us to answer this question with confidence. Our model assumes that they are substitutes, but that's not based on anything we infer from the data.

Our model is certainly not exactly correct, in the sense that there should be some complementarity between compute and algorithms, but the complementarity probably only becomes noticeable for extreme ratios between the two contributions. One way to think about this is that we can approximate a CES production function

$$Y(C,A)=(\alpha C^{\rho }+(1-\alpha )A^{\rho }{)}^{1/\rho }$$

in training compute $C$ and algorithmic efficiency $A$ when $C/A\approx 1$ by writing it as

$$Y(C,A)=AY(e^{\log \left(C/A\right)},1)=A(\alpha e^{\rho \log \left(C/A\right)}+(1-\alpha ){)}^{1/\rho }\approx A(1+\alpha \rho \log \left(C/A\right){)}^{1/\rho }\approx C^{\alpha }{A}^{1-\alpha }$$

which means the first-order behavior of the function around $C/A\approx 1$ doesn't depend on $\rho$, which is the parameter that controls complementarity versus substitutability. Since people empirically seem to train models in the regime where $C/A$ is close to $1$ this makes it difficult to identify $\rho$ from the data we have, and approximating by a Cobb-Douglas (which is what we do) does about as well as anything else. For this reason, I would caution against using our model to predict the performance of models that have an unusual combination of dataset size, training compute, and algorithmic efficiency.

In general, a more diverse dataset containing models trained with unusual values of compute and data for the year that they were trained in would help our analysis substantially. There are some problems with doing this experiment ourselves: for instance, techniques used to train larger models often perform worse than older methods if we try to scale them down. So there isn't much drive to make algorithms run really well with small compute and data budgets, and that's going to bias us towards thinking we're more bottlenecked by compute and data than we actually are.