Symbol hats

The passage around this formula

Reframe the object. A benchmark score $\hat{s}$ is an estimator of a population quantity s — the model’s success rate over some distribution of tasks $\mathcal{D}$ that somebody hopes resembles the work you actually have. Every property that makes an estimator trustworthy applies: $\hat{s} = \frac{1}{n}\sum_{i=1}^{n} \mathbf{1}\!\left[\,\text{success on } x_i\,\right], \qquad x_i \sim \mathcal{D}_{\mathrm{bench}}$. The number is only as good as three things: whether $\mathcal{D}_{\mathrm{bench}}$ resembles $\mathcal{D}$ , whether the $x_i$ are genuinely held out, and whether the indicator is measured with enough repetition to characterise its spread. All three fail routinely, and they fail in different directions.

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