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Equation 7 · Part 6 · Running an Interpretability Investigation That Holds Up

=

Δ(C)=m(Mclean→C←corrupt)−m(Mclean).\Delta(\mathcal{C}) = m\big(M_{\mathrm{clean} \to \mathcal{C} \leftarrow \mathrm{corrupt}}\big) - m\big(M_{\mathrm{clean}}\big).
=

What this part means

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

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Once the question is scoped, the experiment that tests it is a causal one by convention in this field, and the convention exists for a good reason: a component correlated with a behaviour has told you nothing about whether the model uses it, while a component that changes the behaviour when intervened on has told you something. The standard instrument is activation patching — running the model on a clean input, running it again on a corrupted one, then substituting the corrupted run’s activations into the clean run at a chosen set of components C\mathcal{C} and measuring the change in some behavioural metric m : Δ(C)=m(Mclean→C←corrupt)−m(Mclean)\Delta(\mathcal{C}) = m\big(M_{\mathrm{clean} \to \mathcal{C} \leftarrow \mathrm{corrupt}}\big) - m\big(M_{\mathrm{clean}}\big). The choice buried inside that formula — what counts as…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.