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Equation 4 · The Benchmarks That Don't Need the Image

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MG=Sv−Swv,ML=max⁡(0, Swv−St)MG = S_v - S_{wv}, \qquad ML = \max(0,\ S_{wv} - S_t)

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Inputs and operationsS_v - S_wv, qquad ML = max(0, S_wv - S_t)
Result or conditionMG
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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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MM

Symbol M

M is the quantity selected or evaluated by the optimization written on the right.

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GG

Symbol G

G is the quantity selected or evaluated by the optimization written on the right.

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SvS_v

Symbol S_v

SvS_v appears in the objective or constraint used by the optimization on the right.

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SwvS_{wv}

Symbol S_wv

the accuracy on the same items with the image withheld.

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LL

Symbol L

L appears in the objective or constraint used by the optimization on the right.

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StS_t

Symbol S_t

the accuracy of that same model’s underlying text-only language backbone.

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=

=

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

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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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

The first is measurement-time ablation : take an already-trained system, rerun the exact same benchmark items with one channel removed at inference, and compare. This is what the original VQA paper did with its question-only baseline [ 1 ] , and it is what a 2024 audit of vision-language benchmarks did formally, by defining two paired metrics from three separately measured accuracies. Let SvS_v be a model’s accuracy on a benchmark with the image present, SwvS_{wv} its accuracy on the same items with the image withheld, and StS_t the accuracy of that same model’s underlying text-only language backbone, evaluated on its own before any multimodal training touched it. The audit’s two metrics are then…
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The first is measurement-time ablation : take an already-trained system, rerun the exact same benchmark items with one channel removed at inference, and compare. This is what the original VQA paper did with its question-only baseline [ 1 ] , and it is what a 2024 audit of vision-language benchmarks did formally, by defining two paired metrics from three separately measured accuracies. Let SvS_v be a model’s accuracy on a benchmark with the image present, SwvS_{wv} its accuracy on the same items with the image withheld, and StS_t the accuracy of that same model’s underlying text-only language backbone, evaluated on its own before any multimodal training touched it. The audit’s two metrics are then MG=Sv−Swv,ML=max⁡(0, Swv−St)MG = S_v - S_{wv}, \qquad ML = \max(0,\ S_{wv} - S_t). where MG , Multimodal Gain, is how much the image actually added once everything else is held constant, and ML , Multimodal Leakage, is the part of the no-image score that exceeds what the model’s own text backbone could already do unaided — evidence not that the benchmark is answerable from language in general, but that this specific model’s multimodal training pipeline let benchmark answers leak in through some channel other than genuine visual grounding [ 10 ] . The distinction matters because the two problems have different remedies: a benchmark with low MG needs harder, more vision-dependent items; a model with high ML needs a cleaner training pipeline. Collapsing both into a single “the model cheated” headline erases exactly the information a fix would require.

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