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No—not as if they were measurements under the same conditions. A token budget changes the evaluation setting, so report pass rates for each budget tier separately. If a single summary is necessary, state the weights and the deployment mix they represent, and keep the tier-level results visible.
What pass@k measures
Pass@k estimates the chance that at least one of k sampled attempts is correct, averaged across benchmark problems. In the estimator described in the Findings of NAACL 2025 paper, each problem has n collected samples, of which c are correct, with n at least as large as k. The resulting benchmark score is an average of per-problem estimates under the sampling conditions used.
That average does not make results from different token budgets interchangeable. A pass rate is meaningful only with its evaluation conditions: the model and checkpoint, task set and scorer, sampling method, decoding settings, budget, and number of attempts. Keep those details attached to the score.
Why unequal token budgets should stay separate
A larger input-token budget can let a model process more context; an output or reasoning-token limit can constrain what it generates. Changing either may change the measured operating point. An average across budget tiers can therefore blur which conditions produced the score, and may not describe any one of them.
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BudgetBench illustrates a way to evaluate input budgets: its 2026 pilot protocol sweeps 2K, 4K, 8K, 16K, and 32K input-token tiers while holding the model, task, sampler, and decoding settings fixed. It records quality alongside budget utilization, latency, and budget-violation rates. The authors characterize their results as pilot studies and leave the direction of budgeted-versus-full-context performance unresolved; the protocol supports explicit tier reporting, not a claim that one tier is best. See BudgetBench.
How to report a fair comparison
- Show each budget tier. Give a separate pass rate for every input-token budget and, where applicable, every output or reasoning-token limit.
- Hold other conditions fixed when testing budget. Keep the model, task set, scorer, sampler, and decoding settings the same so the budget is the variable under examination.
- State the sampling depth. Report the target k and the actual number n of rollouts collected per problem. Include the pass@k estimator or protocol used.
- Report budget use and compliance when measured. A nominal limit is not enough if runs use different amounts or exceed it; include utilization and violation rates, as well as latency or cost when relevant to the decision.
- Keep any pooled score secondary. If a single aggregate is needed, define its weights from the intended deployment mix, explain what population of budget conditions the result represents, and retain the tier-level scores. There is no universal weighting rule established by the cited protocols.
A useful comparison table should identify the model or checkpoint, task set and scorer, input-token budget, output or reasoning-token budget if applicable, k, collected n, sampler and decoding settings, and budget-use or cost measures. These are reporting recommendations drawn from the conditions the cited evaluations make explicit, not a universal benchmark standard.
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Do not confuse direct pass@k with extrapolation
Direct pass@k is supported by observed per-problem rollouts when k is no greater than the collected sample count n. Estimating pass@k for k greater than n requires assumptions about unobserved outcomes; it should not be presented as a direct measurement.
In a September 8, 2026 arXiv preprint, Singh and Singh argue that fixed-rollout results identify direct pass@k for k ≤ n, but do not identify generic extrapolated pass@k beyond that depth without further assumptions. Their counterfactual example with n=16 found failure at k=1000 ambiguous by factors from 1.5 to over 2,600 across four configurations involving MATH, GSM8K, and CodeContests. That range is specific to their study, not a general error bound. See What Fixed-Rollout pass@k Evaluations Can Identify.
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Practical rule
Compare like with like: keep the budget tier visible, isolate budget changes from other evaluation changes, and label extrapolations as extrapolations. Pool results only when the weighting answers a defined deployment question—not to make unequal conditions look equivalent.
Quick Recap
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