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The passage around this formula

Second, the meaning of a fixed number drifts, and quickly . Ho and colleagues, analysing more than two hundred language-model evaluations from 2012 to 2023, estimated that the compute required to reach a set performance threshold has halved roughly every eight months, with a 95% confidence interval of about five to fourteen months [ 19 ] . If a threshold is fixed at $C^{*}$ and efficiency improves with a halving time $\tau$ , the capability reachable below the threshold grows as though the budget were expanding: $C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}$. The analysis that follows is mine rather than the authors’. Taking the central estimate at face value, a threshold left unamended for two years admits models with…

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