Equation 12 · Part 1 · Frontier AI Model Comparisons: A First-Principles Introduction

Symbol a_true

a_{\mathrm{true}}

a_{\mathrm{true}}

What this part means

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

Its job in the formula

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

Full expressionSymbol a_trueArticle meaning

The passage around this formula

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 bad faith on anyone’s part; it follows from the measurement being taken at all.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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