Who Thinks Best Depends on How Long You Let Them: Budget-Dependent Rankings in LLM Evaluation

Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks ($p {<} 0.01$, McNemar). (iii) Oracle analysis reveals model complementarity up to $+27.8$pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain ($+1.6$ to $+5.7$pp) but are domain-specific and hurt transfer ($-1.2$pp). These results argue for budget-conditioned evaluation protocols.

Mind the Cap: Output-Budget Regimes Change the Measured Multilingual Reasoning Gap

Multilingual evaluations report accuracy at a single output-token cap, but languages need different numbers of tokens to express the same content, so the cap is a hidden experimental variable. We test whether the native-vs-translate gap on MGSM (German, Thai, Swahili) is a token-budget artifact for Qwen3-8B and Llama-3.1-8B-Instruct under four prompting strategies. The measured gap swings by up to 57 points across budgets, length normalization moves it by up to 38.9 points where the cap binds, and at tight caps normalization can reverse which strategy scores higher. We prospectively froze the sweep's three Qwen peaks and its near-zero value at 1024 and evaluated them on 540,000 independently hard-capped decodes: a second frozen family of six Holm-corrected tests rejects every null. The frozen test at $B^*=1024$ still fails to reject because native accuracy has already saturated there; above saturation, the residual difference is a strategy-performance gap, not an identified reasoning deficit. The same truncation channel prices a cost-ordered adaptation ladder: a cross-fitted Thai vocabulary extension closes 0.0 points of the gap at the frozen budget and 4.9 points where 19% of traces still truncate. A third frozen family varies only the announced budget at a fixed enforced cap; announcing 128 rather than 2048 tokens moves Thai native accuracy by 5.1 points, so accuracy is not a function of the enforced cap alone. A correct-emission timing identity computed from one long-cap run matches the three pre-specified MGSM peaks to 0.65 points and, in an exploratory Qwen-only analysis of three further benchmarks, tracks held-out items to 0.92 points, locating the peak exactly in five of seven cells. Treat the output cap as an independent variable and report accuracy across the budget regime, not at a single budget.

Sample More, Reflect Less: Self-Refine and Reflexion Lose to Repeated Sampling at Equal Token Cost, from 1.5B to 7B

Methods that make a language model plan, criticise and rewrite its own answer, reflect on mistakes, pick the best of several attempts, or debate with copies of itself nearly all make it generate far more text than a single chain of thought. Because generating more text raises accuracy by itself, a gain over one chain of thought does not show the method's idea is what helped. Wang et al. (2024) reported that a simple baseline, sampling the same question repeatedly and keeping the most common answer, often wins once budgets are comparable, but gave point estimates with no confidence intervals or significance tests. We rerun that comparison as a designed experiment: seven methods, open models of 1.5B, 3B and 7B parameters, two mathematics benchmarks, 150 questions each. We count every generated token, including those spent on critiques, reflections, debate turns and checking, and compare each method against repeated sampling at its own measured cost. All 36 comparisons are paired by question, with bootstrap intervals and multiplicity correction. No method is reliably better than repeated sampling at equal cost anywhere. Ten are reliably worse, all of them methods where the model inspects its own output, and all 18 self-inspection comparisons are negative. The two kinds of self-inspection part company as models grow. Choosing stops hurting: taking Best-of-N's eight samples and just counting the most common answer beats letting the model pick by 8.0 and 11.3 points at 1.5B, but only 2.0 and 1.3 at 7B, no longer distinguishable from zero. Rewriting does not recover: Self-Refine and a forced Reflexion stay 3.6 to 10.1 points below baseline at 7B. Reflexion as published never triggered its own retry on the smallest model. It judged itself correct every time and silently became a single chain of thought. We release code, prompts, all generations, and our verification scripts.