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Equation 10 · Part 1 · Running an Interpretability Investigation That Holds Up

Symbol S

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

What this part means

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

Its job in the formula

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

The passage around this formula

…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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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