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Equation 12 · Part 5 · How Benchmark Contamination Actually Works in Agentic Evaluation

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passdeterministick=pass1for every k.\text{pass}^k_{\text{deterministic}} = \text{pass}^1 \quad \text{for every } k .
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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.

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 passk\text{pass}^k ≈\approx pkp^k , 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 passdeterministick=pass1for every k\text{pass}^k_{\text{deterministic}} = \text{pass}^1 \quad \text{for every } k . A degenerate exploit is not merely invisible to pass@1; it is more invisible to passks^k, precisely because passks^k was built to reward consistency, and a fixed, checker-satisfying non-answer is the most consistent…

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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.

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Sources cited in the article section

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