When Independent Sampling Outperforms Agentic Reasoning

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from \emph{how much} compute to spend, to \emph{where} to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes \emph{thought-level beam search}. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7% absolute accuracy gain on HMMT-24 and +3.3% on AIME-25 over pruning baselines, delivers $>2\times$ higher throughput on trace completion, and reduces total token consumption by up to 68.5% relative to standard parallel sampling.

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.

Reasoning language models increasingly use test-time compute to improve performance, but existing evaluations typically study this compute one question at a time. Yet when multiple problems share an end-to-end cost or latency constraint, models must decide how to divide limited inference compute among them. We introduce an exam-style evaluation framework for studying this setting, in which a model must distribute one shared token budget across questions with different difficulty and point values to maximize its total score. Across several open and frontier reasoning models, we find that models fail to allocate a shared budget strategically across questions of varying difficulties and values. Models behave largely as greedy sequential solvers: they prioritize questions by presentation order, front-load effort on early questions, and remain insensitive to value, with these tendencies becoming more pronounced as the number of questions grows. Explicit planning prompts spread compute more evenly but do not produce value- or difficulty-aware prioritization. The same behavioral pattern extends from mathematical to code reasoning. These findings establish global budget allocation as a distinct capability that is not captured by conventional per-question evaluation and remains a challenge for current reasoning models.