Equation 7 · Part 4 · Frontier AI Model Comparisons: A First-Principles Introduction

Symbol varepsilon_config

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

\varepsilon_{\mathrm{config}}

What this part means

noise contributed by harness, prompt, effort level, and grading choices, which can push the observed score in either direction.

Its job in the formula

varepsilo $n_c$ onfig is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol varepsilon_configArticle meaning

Where the article explains it

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.

The passage around this formula

…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…

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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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