Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning

A new optimization framework called Uncertainty-Aware Budget Allocation (UAB) reallocates a fixed sampling budget to improve language model reasoning, according to a paper published on arXiv [1]. The method uses per-question uncertainty estimates to shift compute away from easy questions and toward harder ones, requiring no additional model calls [2]. The framework operates in two phases. In the first phase, every question receives one generation. The average negative log-likelihood (ANLL) is extracted directly from output log-probabilities, serving as a difficulty signal while the generation contributes to the final vote [2]. In the second phase, a marginal-greedy algorithm allocates the remaining budget by solving a concave coverage-maximization surrogate exactly. Uncertain questions receive more sampling budget, while confident questions receive fewer additional samples [2]. The authors describe UAB as a concave integer optimization framework [1]. The researchers evaluated UAB on six open-weight and black-box models ranging from 1.5 billion to 27 billion parameters [1]. Testing covered five reasoning benchmarks spanning math, logic, and preference tasks [2]. UAB outperformed baselines by up to 3% in average accuracy and up to 5% on individual benchmarks, with the largest gains observed in low-resource settings [1]. The method requires no auxiliary model or additional LLM call [2]. Code is publicly available on GitHub [1]. Sampling multiple responses is a known technique for improving language model reasoning, but uniform compute allocation is inefficient because easy questions are over-sampled while hard questions remain under-explored [2]. The UAB framework addresses this imbalance by estimating uncertainty at no additional inference cost [1]. The paper was submitted on 26 May 2026 to the Computation and Language section of arXiv [1]. High-quality datasets are integral to machine learning research, and major advances can result from improvements in learning algorithms, computer hardware, and the availability of training data [3]. The UAB evaluation relied on established reasoning benchmarks, though the specific benchmark names were not enumerated in the paper abstract [2]. The arXiv platform, where the paper appears, supports experimental projects through its arXivLabs framework, which allows collaborators to develop and share new features directly on the website [1].