Equation 7 · Part 5 · Frontier AI Model Comparisons: A First-Principles Introduction

=

s_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}},

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article meaning

The passage around this formula

A slightly more general way to see the same point: any observed score can be written as $s_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}}$ . where $a_{\mathrm{true}}$ is the capability the benchmark intends to measure, $\delta_{\mathrm{contam}}$ $\geq$ 0 is a one-directional inflation term from training-set overlap, and $\varepsilon_{\mathrm{config}}$ is noise contributed by harness, prompt, effort level, and grading choices, which can push the observed score in either direction. Two systems’ $s_{\mathrm{obs}}$ values can differ substantially even when their $a_{\mathrm{true}}$ values are identical, and can appear equal even when their $a_{\mathrm{true}}$ values are not, purely through the other two terms. Nothing about this requires…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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