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Equation 7 · Part 8 · Running an Interpretability Investigation That Holds Up

subscript

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).
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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