Equation 13 · 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 C
C 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
A patching experiment produces two different kinds of statement, and the write-up has to keep them visibly separate. The first is a measurement: intervening on component set moved metric m by some amount, with some variance across prompts and random seeds, and the matched control ' moved it by some smaller amount. That is data. The second is an interpretation layered on top of it: that the component “represents,” “detects,” or “computes” some human concept. The measurement is usually solid. The interpretation is usually the part doing more work than the evidence supports, and it is the part press coverage and even conference talks tend to keep while dropping every…
Read the full surrounding passage
A patching experiment produces two different kinds of statement, and the write-up has to keep them visibly separate. The first is a measurement: intervening on component set moved metric m by some amount, with some variance across prompts and random seeds, and the matched control ' moved it by some smaller amount. That is data. The second is an interpretation layered on top of it: that the component “represents,” “detects,” or “computes” some human concept. The measurement is usually solid. The interpretation is usually the part doing more work than the evidence supports, and it is the part press coverage and even conference talks tend to keep while dropping every qualifier attached to it.
Sources cited in the article section
- [11] Open Problems in Mechanistic Interpretability ↗
- [13] Black-Box Access is Insufficient for Rigorous AI Audits ↗
These citations give research context. Read each source to check which claims it supports.
Return to Running an Interpretability Investigation That Holds Up