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Equation 10 · Part 5 · Running an Interpretability Investigation That Holds Up

subtraction

S(C,C′)=Δ(C)−Δ(C′).S(\mathcal{C}, \mathcal{C}') = \Delta(\mathcal{C}) - \Delta(\mathcal{C}').
subtraction

What this part means

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

Its job in the formula

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

The passage around this formula

The defence against this is a control condition run alongside the target one, not after it: intervene identically on a component set C\mathcal{C}' matched to the target set C\mathcal{C} in size, depth and baseline activation statistics, but which the hypothesis explicitly predicts should have no effect, and compare S(C,C′)=Δ(C)−Δ(C′)S(\mathcal{C}, \mathcal{C}') = \Delta(\mathcal{C}) - \Delta(\mathcal{C}'). A specificity margin S that is small relative to the run-to-run variance means the intervention is detecting generic sensitivity to perturbation somewhere in the network, not the mechanism under test — which is exactly the failure mode the subspace illusion exhibits. Reporting Δ(C)\Delta(\mathcal{C}) alone, without the matched control alongside it, is reporting half…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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