Equation 5 · Part 2 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
where pass@ k is the probability that at least one of k attempts succeeds, and pass ^k is the probability that all k succeed [ 3 ] . The two statistics move in opposite directions as k grows: pass@ k climbs toward certainty, which is the right question when a system can retry until something works or a human picks the best of several drafts, while pass ^k falls toward zero, which is the right question for an agent deployed without a human standing by to catch the failures. Yao and colleagues report that state-of-the-art function-calling agents solved under half of τ-bench’s tasks on a single attempt, and that their pass ^k scores fell substantially with repeated trials of the same task under…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.