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Equation 20 · Part 1 · How Mechanistic Interpretability Research Is Actually Done

Symbol c

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).
cc

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

…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 much of the clean behaviour component c can restore on its own. The complementary direction, a corrupted value spliced into an otherwise clean run, is noising, and it measures how much clean behaviour depends on c specifically. The two ask different questions, and a careful study reports both, together with the exact corruption and the…

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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

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