Uncertainty-Aware Budget Allocation Improves Sampling Efficiency in LLM Reasoning
ORIGINAL / Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning
This work proposes Uncertainty-Aware Budget Allocation (UAB), which estimates difficulty from vote entropy of initial samples and reallocates a fixed generation budget toward questions with high answer disagreement. Compared with uniform allocation, UAB improves average accuracy by 2.3% and up to 5.5% on individual benchmarks across five open-weight models and five reasoning benchmarks, with the largest gains in low-resource settings and no extra model calls.
01 ABSTRACT
The paper notes that uniform sampling of multiple responses for language model reasoning is inefficient: easy questions are over-sampled while hard questions remain under-explored. UAB first generates a small fixed number of samples per question and uses their vote entropy as a difficulty signal, then allocates the remaining budget to questions with high disagreement via marginal-greedy concave optimization. Reported results show an average accuracy gain of 2.3% over uniform allocation across five open-weight models (1.5B–27B) and five reasoning benchmarks, with up to 5.5% on individual benchmarks and the largest gains in low-resource settings.
02 KEY FINDINGS
- UAB operates in two phases: a small fixed initial budget yields vote entropy as a difficulty signal, then marginal-greedy allocation assigns the remaining budget to questions with high answer disagreement.
- Across five open-weight models and five reasoning benchmarks, UAB improves average accuracy by 2.3% over uniform allocation under a fixed total budget, with up to 5.5% on individual benchmarks.
- It requires no auxiliary model or additional LLM calls, meets the target budget exactly, and shows larger gains for low-resource models.
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