Methodology
The page reports the output of a simulation model that is re-run whenever new evidence is logged. Nobody sets the needle by hand. All forecasts are conditional on no deliberate slowdown or pause.
The model
We simulate many possible trajectories of frontier AI capability, measured on a scale like Epoch AI's Capabilities Index (ECI). Each trajectory has its own sampled parameters and random shocks.
Feedback loop. Capability produces an R&D uplift, and uplift speeds up capability growth:
uplift U = U_ref × 2^((C − 170) / k) (at least 1), and dC/dt = g0 × U(t − lag)^λ × shock.
Higher capability raises uplift; higher uplift raises the growth rate. That loop is what makes this a model of recursive self-improvement rather than a trend line. λ below 1 captures diminishing returns: compute bottlenecks and ideas getting harder mean that doubling research labour less than doubles progress.
Stages are read off uplift. Stage 2 begins when the AI-attributable acceleration of capability progress, U^λ, reaches 1.3× (provisional). Stages 3, 4 and 5 begin at sampled uplift thresholds U3 < U4 < U5, with stage 4 centred near the 25× software R&D uplift used by the AI Futures Project.
Evidence. Every logged observation has a noise model. Trajectories are weighted by how well they match all observations published on or before a given day, the same approach the AI Futures Project uses for its "filtered" runs. Replaying this for every day since January 2024 produces the arrival-date graph.
To keep enough trajectories in play as evidence accumulates, we sample from an adaptive mixture: the prior plus Gaussians fitted to pilot runs, corrected with exact importance weights. This takes the place of resampling. The effective sample size is reported with each run.
Three different "multipliers"
Sources report three different quantities that all get called acceleration. The model treats each as a separate noisy observation of the hidden state:
| Quantity | Maps to | Noise |
|---|---|---|
| AI-attributable acceleration of capability progress (METR) | U(t − lag)λ | Stated range + reliability floor |
| Software R&D uplift (AI Futures Project) | U(t) | Stated range + floor |
| Self-reported labour uplift (staff polls) | U(t)ρ | Large: "only very loose evidence" |
| Public frontier ECI (Epoch) | C(t − internal/public gap) | Epoch CI + 3.5 points |
| METR 50% time horizon | ECI-equivalent via a fitted log-linear map | Residual sd, doubled from mid-2026 |
| Anthropic R&D Automation Index shares | Logistic in log₂ U | Logit-scale; zeros treated as "at or below 3%" |
Priors
| Parameter | Meaning | Prior 10%–90% | Posterior 10% / 50% / 90% |
|---|
Validation
There is no ground truth for the headline until it happens, so validation is indirect.
Comparison with the AI Futures Project
Cross-checks
Five simple extrapolations from the AI Futures Project, shown as a sanity panel. They are not model inputs.
Backtest
Sensitivity
How the stage 4 median moves when we change one thing.
Known weaknesses
- The strongest evidence is a single lab's partly redacted disclosure. One report can move the needle by months; the sensitivity table shows by how much.
- Public releases may understate internal capability. Anthropic says it deliberately limited AI-R&D-relevant capabilities in Fable 5.2 and Mythos 5.2.
- Acceleration may be confined to well-specified, benchmarkable tasks. If so the model runs early. The Remote Labor Index (real-world freelance tasks) is logged as a check on this.
- The stage boundaries are our definitions. The stage 1 to 2 boundary (1.3×) is provisional.
- No lab other than Anthropic publishes a quantified R&D automation measure, so the needle is anchored on the lab that discloses most.
- Publication dates for benchmark records are approximated as model release plus 14 days.
- Some inputs share evidence. The AI Futures Project's 3.1× software-uplift estimate is derived from METR's assessment, and METR drew on Anthropic's internal index, which is also logged. That is partly why dropping the METR report alone barely moves the median. We remove exact restatements (see the
model_usecolumn of the log) but not every correlation. - The Anthropic R&D Automation Index is the most influential single input, and every month of it was first published on 17 September 2026. A series read from one chart is counted as roughly three independent observations, not one per month.
- The priors were set in November 2026, partly using calibration figures published then (for example "stage 4 ≈ 25× uplift"). Replayed forecasts for 2024–2025 therefore use only the evidence available on each day, but priors chosen with hindsight.
- Superseded evidence is not erased from history: the AI Futures Project's August 2026 uplift estimates count until their November revision was published, then stop counting.
Sources
- Epoch Capabilities Index:
epoch.ai/data/eci_scores.csv(CC-BY) - METR time horizons:
metr.org/assets/benchmark_results_1_1.yaml(last updated May 2026; no longer maintained) - METR, assessment of AI R&D acceleration at Anthropic (5 Nov 2026)
- Anthropic R&D Automation Index, system cards and risk reports
- AI Futures Project timelines updates (comparison lines only; feeding their forecasts into our model would double-count evidence)
- TasteVal (P-Zero Research) and the Remote Labor Index: cross-checks, not model inputs
Download the full observation log: every value, its source, quote, publication date and approver.