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Equation 7 · Part 2 · What a Circuit Explains: The State and Limits of Mechanistic Interpretability

Symbol C

Δ(C)=m ⁣(Mclean with C set to aCcorrupt)−m ⁣(Mclean).\Delta(\mathcal{C}) = m\!\left(M_{\mathrm{clean}} \text{ with } \mathcal{C} \text{ set to } a_{\mathcal{C}}^{\mathrm{corrupt}}\right) - m\!\left(M_{\mathrm{clean}}\right).
C\mathcal{C}

What this part means

C is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

C is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…model on a clean input, run it on a corrupted one, then substitute the activations of a chosen component from one run into the other and measure the change in some behavioural metric. Formally, for a set of components C\mathcal{C} and a metric m , Δ(C)=m ⁣(Mclean with C set to aCcorrupt)−m ⁣(Mclean)\Delta(\mathcal{C}) = m\!\left(M_{\mathrm{clean}} \text{ with } \mathcal{C} \text{ set to } a_{\mathcal{C}}^{\mathrm{corrupt}}\right) - m\!\left(M_{\mathrm{clean}}\right). Meng and colleagues used a version of this — causal tracing — to localise factual recall, finding that a distinct set of steps in middle-layer feed-forward modules mediate factual predictions at the subject token, and then used the localisation to…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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