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Equation 20 · Part 7 · How Mechanistic Interpretability Research Is Actually Done

=

Patch(c)=m(M(xcorrupt; ac←acclean))−m(M(xcorrupt)).\mathrm{Patch}(c) = m\Big(M\big(x_{\mathrm{corrupt}};\ a_c \leftarrow a_c^{\mathrm{clean}}\big)\Big) - m\big(M(x_{\mathrm{corrupt}})\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

The standard instrument is activation patching. Run the model once on a clean input and once on a deliberately corrupted variant of it — a single token changed, a name swapped — caching every intermediate activation from both runs. Then run the model a third time on the corrupted input, but with one chosen component’s activation overwritten by the value it took during the clean run, and measure the resulting change in some scalar behavioural metric m , typically the gap between the correct answer’s logit and a specific incorrect competitor’s logit: Patch(c)=m(M(xcorrupt; ac←acclean))−m(M(xcorrupt))\mathrm{Patch}(c) = m\Big(M\big(x_{\mathrm{corrupt}};\ a_c \leftarrow a_c^{\mathrm{clean}}\big)\Big) - m\big(M(x_{\mathrm{corrupt}})\big). This particular direction — a clean value spliced into an otherwise corrupted run — is called denoising: it measures how…

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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.