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Equation 7 · Part 3 · Frontier AI Model Comparisons: A First-Principles Introduction

Symbol delta_contam

sobs=atrue+δcontam+εconfig,s_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}},
δcontam\delta_{\mathrm{contam}}

What this part means

deltaca_contam is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

deltaca_contam is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

A slightly more general way to see the same point: any observed score can be written as sobs=atrue+δcontam+εconfigs_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}}. 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…

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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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