Feb 2, 2026

The Half-Life of Compute Thresholds

Aaron Potter

ompute thresholds are widely discussed as a practical governance tool, but the literature

rarely specifies how quickly fixed thresholds become outdated as algorithmic efficiency improves.

We develop a compute-threshold staleness model that distinguishes raw training compute from

baseline-equivalent (“effective”) compute and defines staleness as the ratio between a policy

threshold and the time-varying threshold that would remain aligned with a fixed risk cutoff

Reviewer's Comments

Reviewer's Comments

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The model's most significant limitation is the assumption that τ is constant across domains and over time. Algorithmic efficiency likely improves at different rates for different capability types (language understanding vs. code generation vs. chemistry), which means a single threshold update cadence may be insufficient — the paper should explore domain-specific τ values and their policy implications. The backtest, while a nice touch, confirms consistency with Ho et al.'s estimates rather than providing independent validation, since the model's dynamics depend on those same estimates.

Not clear on counterfactual impact of this work; doubling time only, without these formulae, already provides "a simple model which can provide a good intuitive grasp of the problem for policy-makers." In practice, this model may be making the the explanation more opaque to policymakers.

There could be some value in describing staleness in the intervals between doubling times; e.g how stale is the threshold at 7 months with an 8 month doubling time; but this still can be reasoned about pretty intuitively with knowledge of the doubling time, and a simple, one-off calculation.

I would want to see more exploration or elaboration on specific use-cases for this work to better understand its impact potential. Maybe dealing with uncertainty around doubling time, or enabling very precise update thresholds under certain conditions.

Cite this work

@misc {

title={

(HckPrj) The Half-Life of Compute Thresholds

},

author={

Aaron Potter

},

date={

2/2/26

},

organization={Apart Research},

note={Research submission to the research sprint hosted by Apart.},

howpublished={https://apartresearch.com}

}

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This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.
This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.