Equation 10 · Part 4 · How Benchmark Contamination Actually Works in Agentic Evaluation
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
averaged over tasks to produce the benchmark’s headline number. The metric is designed to punish an agent whose competence is real but inconsistent across resampled trials — a stochastic policy with true per-trial success probability p has , which falls quickly as k grows. But a policy whose output on a given task is deterministic — an empty response, always, regardless of sampling — produces the identical transcript on every trial, so
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 article section
- [8] Establishing Best Practices for Building Rigorous Agentic Benchmarks ↗
- [7] τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains ↗
- [9] Saving SWE-Bench: A Benchmark Mutation Approach for Realistic Agent Evaluation ↗
These citations provide research context; check each source for the exact claim it supports.