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Equation 6 · What Open Weights Actually Let You Verify

What does this equation mean?

f(θ,H)=f(θ′,H′)f(\theta, H) = f(\theta', H')

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Inputs and operationsf(θ', H')
Result or conditionf(θ, H)
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ff

Symbol f

f is part of the quantity the equation computes from the expression on the right.

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θ\theta

Symbol θ

the model’s parameters.

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HH

Symbol H

H is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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How to interpret it

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What the article says around this equation

Here θ\theta denotes the model’s parameters and H denotes everything about the evaluation procedure that is not the model itself — the exact prompt template, the number of few-shot examples, whether a chat template is applied, how the model’s free-text output is parsed into a scored answer, and the decoding configuration. A vendor publishes one value of s . An independent lab computing its own s' is implicitly testing whether f(θ\theta, H) = f(θ\theta', H') , and a mismatch could in principle come from either argument.

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