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Published equation contexts

G(t)=C(t)−V(t),dGdt=dCdt−dVdtG(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}

Why this formula appears here

Whether the documented gap between capability and verified safety narrows or widens is not a third axis; it is what the other two jointly produce. Write C(t) for a stylised index of frontier capability — METR’s time-horizon trend is the best-measured available proxy [ 16 ] — and V(t) for an index of independently checkable verification coverage: the share of a system’s decision-relevant behaviour that something other than watching its output can vouch for. The gap is G(t)=C(t)−V(t),dGdt=dCdt−dVdtG(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}. The gap narrows exactly when verification coverage grows faster than capability does. Axis A determines whether d\mathrm{d}V/d\mathrm{d}t can be large at all — whether there is a technique to scale in the…

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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G(t)=C(t)−V(t),dGdt=dCdt−dVdt.G(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}.

Equation 3 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Whether the documented gap between capability and verified safety narrows or widens is not a third axis; it is what the other two jointly produce. Write C(t) for a stylised index of frontier capability — METR’s time-horizon trend is the best-measured available proxy [ 16 ] — and V(t) for an index of independently checkable verification coverage: the share of a system’s decision-relevant behaviour that something other than watching its output can vouch for. The gap is G(t)=C(t)−V(t),dGdt=dCdt−dVdtG(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}. The gap narrows exactly when verification coverage grows faster than capability does. Axis A determines whether d\mathrm{d}V/d\mathrm{d}t can be large at all — whether there is a technique to scale in the…

Meanings in this article

  • VV: the field-wide growth rate of.
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