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Equation 7 · Part 9 · What a Circuit Explains: The State and Limits of Mechanistic Interpretability

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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).
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The standard instrument is activation patching : run the 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 perform rank-one weight edits that changed specific facts [ 14 ] . The edit is the strongest form of the argument: a…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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