Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916049452007424 |
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| author | Nguyen, Manh Gupta, Sunil Le, Hung |
| author_facet | Nguyen, Manh Gupta, Sunil Le, Hung |
| contents | Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget based on per-question uncertainty estimated at no additional inference cost. In Phase 1, every question receives one generation; its average negative log-likelihood (ANLL), extracted directly from output log-probabilities, serves as a difficulty signal while the generation contributes to the final vote. In Phase 2, the remaining budget is allocated by a marginal-greedy algorithm that solves a concave coverage-maximization surrogate exactly: uncertain questions receive more sampling budget while confident questions receive fewer additional samples. Evaluated on six open-weight and black-box models spanning 1.5B to 27B parameters and five reasoning benchmarks covering math, logic, and preference tasks, UAB outperforms baselines by up to +3% in average accuracy and up to +5% on individual benchmarks, with the largest gains in low-resource settings, requiring no auxiliary model or additional LLM call. Code is publicly available at https://github.com/manhitv/UAB. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning Nguyen, Manh Gupta, Sunil Le, Hung Computation and Language Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget based on per-question uncertainty estimated at no additional inference cost. In Phase 1, every question receives one generation; its average negative log-likelihood (ANLL), extracted directly from output log-probabilities, serves as a difficulty signal while the generation contributes to the final vote. In Phase 2, the remaining budget is allocated by a marginal-greedy algorithm that solves a concave coverage-maximization surrogate exactly: uncertain questions receive more sampling budget while confident questions receive fewer additional samples. Evaluated on six open-weight and black-box models spanning 1.5B to 27B parameters and five reasoning benchmarks covering math, logic, and preference tasks, UAB outperforms baselines by up to +3% in average accuracy and up to +5% on individual benchmarks, with the largest gains in low-resource settings, requiring no auxiliary model or additional LLM call. Code is publicly available at https://github.com/manhitv/UAB. |
| title | Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2605.26849 |