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Equation 10 · Part 1 · Frontier AI Model Comparisons: A First-Principles Introduction

Symbol varepsilon_config

εconfig\varepsilon_{\mathrm{config}}
εconfig\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

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

Where the article explains it

where atruea_{\mathrm{true}} is the capability the benchmark intends to measure, δcontam\delta_{\mathrm{contam}} ≥\geq 0 is a one-directional inflation term from training-set overlap, and εconfig\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

where atruea_{\mathrm{true}} is the capability the benchmark intends to measure, δcontam\delta_{\mathrm{contam}} ≥\geq 0 is a one-directional inflation term from training-set overlap, and εconfig\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’ sobss_{\mathrm{obs}} values can differ substantially even when their atruea_{\mathrm{true}} values are identical, and can appear equal even when their atruea_{\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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