Doublings in AI software efficiency per doubling of cumulative AI software research input
- Measures
- The number of doublings of AI software efficiency produced by each doubling of cumulative AI software research input: the returns parameter r (lambda over beta) of the semi-endogenous idea-production model fitted to AI software progress.
- Population
- Frontier AI software (training algorithms and methods) in the deep learning era, up to the present.
- Conditions
- Research input is cumulative quality-adjusted research effort; software efficiency is the reduction in compute needed to reach a fixed level of capability; experimental compute is taken as it historically grew, not held fixed.
- Unit
- doublings per doubling
Most likely about 1.2 doublings per doubling; 90% interval 0.40 to 4.0 doublings per doubling.
Stated as a distribution, the precision the evidence supports. right-skewed, roughly log-normal
Assessment
The graph's estimate, all things considered: the figures and arguments it rests on, and how they were combined.
The returns parameter for AI software is poorly pinned down. The published estimates come from a small group of researchers fitting the semi-endogenous growth model to a few series. For image recognition training efficiency, Epoch's estimate of about 1.4 means each doubling of efficiency needed less than double the research effort for the next one. A rough comparison with algorithms in general gives a figure near 4. Forethought's best guess for current frontier LLM software is about 1.2, and it allows that gains in capability, rather than efficiency alone, could raise the true value by about twice. The Stockfish chess engine, as an outside comparison, comes out near 0.83. The estimates are uncertain for several reasons. Researcher counts are a poor proxy for quality-adjusted input. Experimental compute grew alongside researcher labour, which confounds the two. Efficiency series are measured at fixed capability over short spans. The median is set near 1.2, and the 90% interval runs from about 0.4 to about 4. That leaves roughly a 55 to 60% probability that the value is above 1.
The work: which figures, how they were combined, and the arithmetic
The figures used are Epoch's image-recognition estimate (about 1.4), Forethought's current-software best guess (about 1.2), its rough algorithms-in-general figure (about 4, from 28%/7% growth rates), and Stockfish (0.83) as a lower comparison. These were combined judgmentally on a log scale. The median follows the estimate most directly about current frontier software. The tails are widened for confounding by compute growth, the proxy for research input, and the small number of series. Because of budget, the primary Epoch dataset was not re-read in this pass.
Estimates
Each figure a source states for this quantity, in its own words, under the argument it belongs to and read against the graph's estimate.
Grey band: the graph's 90% interval, with its central value as a line. Dark marks: each source's own figure. A thin line is an interval, a thick bar its middle half, a dot a single figure, a dashed arrow a bound. An open box is where an argument places the value.
Claims about where the value lies
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- Each doubling of cumulative AI software research input yields more than one doubling of software efficiency (returns parameter r > 1).InconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →credence 0.55estimate implies ≈ 0.61
Decomposition
This claim has not been assessed yet. Attention goes where its expected value is highest and someone funds it; once this claim's assessment is funded and runs, it may well decompose into subclaims.
Provenance
Where this quantity's evidence comes from. The figures sources state are under Estimates above.
Its one source has been traced to an origin, or to one another.
we might currently expect that a single doubling in cumulative AI software R&D efforts would lead to a few doublings in AI software capacity
Best guess roughly 1 to 4, with high uncertainty, before adjusting for fixed hardware.
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Created by claim_steward · Nov 11, 2026. Every judgment on this page is accompanied by a reasoning trace.