Do the returns to software R&D point towards a singularity?

One critical assumption in this scenario is that progress in the efficiency of AI systems is driven solely by cognitive labor. In practice, it’s likely that experiments play a big role in driving efficiency progress as well, and it’s possible the amount of computation that must be spent on these experiments is not substantially reduced by software progress elsewhere. In this case, this simple model will overstate how strong the case for a software singularity would be.

Using the Stockfish data, we obtain a central estimate of returns to research effort, \(r\), of about 0.83, with a standard error of 0.15. This value of \(r\) is just shy of the threshold of \(1\) that we discussed earlier, though our estimates don’t rule out the returns to research effort exceeding unity. If AI R&D is anything like the R&D involved in building better chess engines, then this provides some weak evidence against “foom”.

With this data, our estimation strategy amounts to performing a Bayesian update with a single data point. Clearly this is far from perfect (e.g. because goodness of fit tests cannot be performed if only one data point is available), but it is still preferable compared to previous approaches used in the literature. Our results are shown in Figure 2 . In all four of these case studies, our median estimates of \(r\) exceed one, but like in computer chess this finding is not statistically significant. Although these case studies suggest a higher chance of \(r>1\) than for computer chess, we place more weight on our estimates from Stockfish since it’s the domain for which we have the best data. Even still, across these (limited) case studies it appears very plausible that the returns to R&D in software are indeed greater than one.

Our work suggests that the returns to research in software are high – in some cases, our estimates are consistent with a proportional increase in research input resulting in a greater-than-proportional software improvement. In contrast, the returns to R&D in other domains might be substantially lower. For example, Bloom et al. (2020) find a value as low as \(r \approx 0.32\) for the aggregate US economy, and our replication of this result yields an even more pessimistic median estimate of \(r \approx 0.25\). This lends more credence to our previous argument, that if we can automate R&D, and simultaneously scale up the amount of compute used to run AI systems, accelerating growth looks likely .

While our estimates are consistent with the possibility of a software singularity, there are reasons to be cautious in interpreting these results as strong evidence for this outcome. Historically, hardware and software progress have improved at similarly rapid rates , suggesting a symbiotic relationship between the two. One explanation is that hardware advancements enable the exploration of more complex algorithmic ideas, some of which lead to improvements in software efficiency. This implies that software R&D progress might be more challenging without concurrent hardware advancements. Therefore, while our findings are consistent with a software singularity, dependence of software progress on hardware progress could block this possibility.

Historically, improvements in software have been significantly influenced by concurrent advancements in hardware, highlighting a symbiotic relationship between the two. This suggests that software R&D improvements might be more challenging in the absence of parallel hardware progress. Consequently, we do not believe the current empirical data provides strong evidence for the possibility of a software singularity.