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Equation 12 · Part 4 · How Benchmark Contamination Actually Works in Agentic Evaluation

subscript

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

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

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

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