Equation 12 · Part 4 · How Benchmark Contamination Actually Works in Agentic Evaluation
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→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 . A degenerate exploit is not merely invisible to pass@1; it is more invisible to pas, precisely because pas was built to reward consistency, and a fixed, checker-satisfying non-answer is the most consistent…
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? 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.