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Equation 7 · Part 6 · What a Circuit Explains: The State and Limits of Mechanistic Interpretability

=

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).
=

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

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 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.