This tool is a simulation companion to How quick and big would a software intelligence explosion be? Alongside the ability to change parameterizations (in the sidebar), users have three main options:
- Multiple Simulations: Run several simulations with uncertainty over key parameters. The output is a table showing the fraction of simulations where the average pace of software progress exceeds a specified threshold over some number of years.
- Single Simulation: Run a single simulation under specific parameter values to illustrate the path of AI progress, including the evolution of diminishing research productivity and growth rates over time.
- Speed-up calculator for when rcog<1: This calculator calculates how many times faster is the (balanced) growth path of software once ASARA is achieved if there is no SIE. This calculator explicitly considers a exponentially growing compute stock and constant value for rcog<1.
Results
How this is calculated
Once AI R&D is fully automated, the “researchers” are AI systems running on compute. Their number scales with inference compute, and their quality rises with the software stock and with training compute — closing a feedback loop (better software → better and more numerous researchers → better software) that raises the balanced-growth rate of software progress. The number above is how many times faster software progresses on the post-automation balanced growth path, assuming a growing compute stock and constant diminishing returns to R&D (rcog held fixed).
1. Research labour before automation. Software progress follows the semi-endogenous law of motion
where CE is experiment compute, α is the labour share, and r is the returns to software R&D. We take the returns to cognitive labour rcog = rα as an input; together with α this pins down the implied r = rcog/α and the returns to compute rcomp = r(1 − α) = rcog(1 − α)/α. On the balanced growth path the law of motion implies
Before automation, research labour is exogenous — it grows at a rate gLbefore set outside the model — so
With the current inputs, gSbefore = —. This is the baseline the speed-up is measured against.
2. Research labour after automation. An automated researcher’s quality grows with the software stock S and with training compute CT, while the number of researchers scales with inference compute CI:
where if you double training compute, γ is how many times you double per-FLOP productivity at runtime, holding software constant.
Quality-adjusted labour is the product of the two. Writing every compute stock as a common aggregate C (they scale together):
The trailing gS term is the automation feedback — research labour now depends on the very software stock it is helping to build.
3. Software growth on the balanced path. As above, on the balanced growth path we have the growth rate of software quality given by
4. Substitute the researcher growth rate. Plugging gL = (1+γ)gC + gS into the balanced-growth condition (point 3) and solving for gS:
or equivalently we have
With the current inputs, gSafter = —. If rcog ≥ 1 the denominator is non-positive, the balanced path breaks down, and you get a software-only intelligence explosion (outside this calculator’s no-SIE scope).
5. The speed-up. Dividing the post-automation rate (step 4) by the pre-automation rate (step 1) gives how many times faster software progresses once AI R&D is automated:
The speed-up grows with γ (higher-quality automated researchers) and as rcog approaches 1 (stronger software feedback), and shrinks the faster pre-automation labour already grew (gLbefore). When pre-automation labour grew at the compute rate (gLbefore = gC) it simplifies to (1 + αγ) / (1 − rcog).