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Equation 4 · Ten Failure Modes That Show Up Across Every Frontier Model, Not Just One

What does this equation mean?

Δcontamination\Delta_{\text{contamination}}

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inflation from the model having seen the benchmark, or something close to it, during training. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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Δcontamination\Delta_{\text{contamination}}

Symbol Delta_contamination

inflation from the model having seen the benchmark, or something close to it, during training.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

Δcontamination\Delta_{\text{contamination}} is inflation from the model having seen the benchmark, or something close to it, during training. Δconfiguration\Delta_{\text{configuration}} is variance from everything about how the question was asked, formatted, and scored — prompt wording, decoding settings, which variant answered. Both terms are provider-specific and time-specific; neither is disclosed by the headline number. Three of the ten failure modes below are different ways that Δcontamination\Delta_{\text{contamination}} and Δconfiguration\Delta_{\text{configuration}} get large without the label on the chart changing.

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