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

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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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C\mathcal{C}

Symbol C

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

Equation 10 · AI Research

Running an Interpretability Investigation That Holds Up

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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