Equation 2 · Running an Interpretability Investigation That Holds Up
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
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.
Read it piece by piece
Symbol k
k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
The reason this ordering matters is not procedural fussiness. Zhang and Nanda’s systematic study of activation patching found that the choice of corruption distribution and evaluation metric — decisions usually made informally, late, and sometimes after a first look at the data — can by itself change which components a patching sweep identifies as important [ 3 ] . If the metric is chosen after the sweep, on the grounds that it produced the most legible result, the investigation has stopped testing a hypothesis and started constructing one to fit the data. The same failure has a clean statistical description. Sweep enough components at a nominal per-test false-positive rate and report…
Read the full surrounding passage
The reason this ordering matters is not procedural fussiness. Zhang and Nanda’s systematic study of activation patching found that the choice of corruption distribution and evaluation metric — decisions usually made informally, late, and sometimes after a first look at the data — can by itself change which components a patching sweep identifies as important [ 3 ] . If the metric is chosen after the sweep, on the grounds that it produced the most legible result, the investigation has stopped testing a hypothesis and started constructing one to fit the data. The same failure has a clean statistical description. Sweep enough components at a nominal per-test false-positive rate and report only the one that clears threshold, and the probability that at least one clears by chance alone across k independently tested components is
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to Running an Interpretability Investigation That Holds Up