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Equation 12 · Part 3 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

Symbol t_0

T50(t)≈T50(t0)⋅2(t−t0)/τ,τ≈7 months,T_{50}(t) \approx T_{50}(t_0)\cdot 2^{(t-t_0)/\tau}, \qquad \tau \approx 7\text{ months},
t0t_0

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t0t_0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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t0t_0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The clearest empirical trend in this area comes from METR, which measured how the length of software tasks that leading agents can complete at even odds has changed over time, expressed as a time horizon T50T_{50} - the length of task, in expert-human time, that an agent completes successfully half the time. Kwa and colleagues report that this time horizon has been doubling roughly every seven months since 2019, which can be written as an empirical fit T50(t)≈T50(t0)⋅2(t−t0)/τ,τ≈7 monthsT_{50}(t) \approx T_{50}(t_0)\cdot 2^{(t-t_0)/\tau}, \qquad \tau \approx 7\text{ months}. and they further find that this trend is driven substantially by improved reliability and error recovery over long horizons, not only by raw single-step capability [ 4 ] . This is a genuinely informative fact and it is also,…

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