Equation 22 · How Mechanistic Interpretability Research Is Actually Done
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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol c
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What the article says around this equation
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 exact metric used, because Zhang and Nanda showed that changing either of those methodological choices can change which components a patching study identifies as important for the same behaviour in the same model — a localisation claim, they…
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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 exact metric used, because Zhang and Nanda showed that changing either of those methodological choices can change which components a patching study identifies as important for the same behaviour in the same model — a localisation claim, they establish, is a claim relative to a stated protocol, not a free-standing fact about the network [ 11 ] .
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