Diminishing returns in the NanoGPT speedrun:

To determine whether we're heading for a software intelligence explosion, one key variable is how much harder algorithmic improvement gets over time. Luckily someone made the NanoGPT speedrun, a repo where people try to minimize the amount of time on 8x H100s required to train GPT-2 124M down to 3.28 loss. The record has improved from 45 minutes in mid-2024 down to 1.92 minutes today, a 23.5x speedup. This does not give the whole picture-- the bulk of my uncertainty is in other variables-- but given this is existing data it's worth looking at.

I only spent a couple of hours looking at the data [3], but there seem to be sharply diminishing marginal returns, which is some evidence against a software-only singularity. 

At first improvements were easy to make without increasing lines of code much, but then improvements became small and LoC required became larger and larger with increasingly small improvements, which means very strong diminishing returns-- speedup is actually sublinear in lines of code. This could be an artifact related to the very large elbow early on, but I mostly believe it.

If we instead look at number of stars as a proxy for amount of attention on the project [4], there are no diminishing returns. The data basically suggest speedup is linear in effort [1], which is consistent with a world where 3x/year increases in labor and compute are required to sustain the historical trend of ~3x/year algorithmic speedups observed by Epoch. However, this still points against a software intelligence explosion, which would require superlinear speedups for linear increases in cumulative effort.

Given that the speedup-vs-stars and speedup-vs-improvement-# graphs are linear but speedup-vs-LoC is sublinear, our guess should be that returns to research output are somewhat sublinear. In the language of Davidson's semi-endogenous growth model, this means $\beta >1$ [2]. Of course there are massive caveats about extrapolation to future models.

In Davidson's model, the requirement for a software intelligence explosion after research is automated is $r:=\frac{\lambda \alpha }{\beta }>1$, where $\lambda <1$ represents inefficiency of parallel work and $\alpha <1$ is the elasticity of research output to cognitive labor at a fixed compute budget. If $\beta >1$, this mathematically means $r<1$ and we don't get an SIE.

So I think an SIE will only happen if one or more of the below is true:

• Cognitive quality of future AIs being so high that one hour of AIs researching is equivalent to exponentially large quantities of human researcher hours, even if they don't train much more efficiently to the same capability level. This is the most important question to answer and something I hope METR does experiments on in Q1.
• Some other difference between nanogpt and frontier AI research, e.g. maybe research ability is easier to improve than base model loss
• Once we get AGI, something other than human labor, AI labor, or compute scales exponentially on a much faster timescale, e.g. training data
• A paradigm shift to a totally different architecture that wouldn't be captured in a dataset only 1.5 years long
• AIs with 2x the efficiency cause research to happen more than 2x faster, despite outweigh the diminishing returns from parallel work AND being bottlenecked by compute, making $\lambda \alpha >1$. I can't think of a way this could happen, and to get an SIE it would have to be even larger than 1.

[1]: This was previously observed in a tweet from Epoch in February but now we have about twice the data.

[2]: $\beta =0$ would mean exponential improvements, while $\beta =1$ implies linear improvement over time at constant labor/compute. So $\beta >1$ means improvements are actually slower than linear.

[3]: A few minutes ideating, almost an hour writing a prompt for Claude 4.5 Opus, then 30 minutes making graphs and such.

[4]: It's unclear whether to say that stars represent instantaneous effort or total cumulative effort on the project. If we interpret it as instantaneous effort, then we would see diminishing returns. Also it's unclear whether stars are measuring $\lambda \beta$ or $\beta$; if $\lambda \beta$ it might imply slightly increasing returns.