Results show that test-time compute can be more effective when used to refine sampled trajectories rather than only to sample more candidates or rely on verifier-guided selection.
Abstract
Test-time scaling improves LLM reasoning by using additional inference compute, but wider sampling alone can suffer from diminishing returns: new rollouts often repeat existing answer patterns instead of adding useful reasoning diversity. Verifier-based selection offers an alternative, but its performance depends on the calibration of an external reward model. We propose a verifier-free breadth--depth refinement framework that uses test-time compute to both explore and improve candidate solutions. The method samples multiple independent reasoning rollouts, refines each rollout through iterative self-critique and self-correction, and aggregates the refined answers by majority voting. Breadth preserves diverse initial attempts, while depth repairs local reasoning errors before aggregation. Across AIME24, AIME25, AMC, OlympiadBench, and MATH500, our method consistently improves over greedy decoding, majority voting, verifier-based best-of-$N$, beam search, and lookahead decoding across multiple open-weight models. For instance, with Qwen2.5-1.5B, accuracy increases from the strongest verifier-based baseline to $58.0\%$ on MATH500, and from $25.0\%$ to $32.5\%$ on AMC. These results show that test-time compute can be more effective when used to refine sampled trajectories rather than only to sample more candidates or rely on verifier-guided selection.
Funnel of Thoughts (FoT) is introduced, an inference-time method that preserves the full 32-trajectory voted accuracy while halving its attention FLOPs, a 28.8% reduction in full-model inference cost.
Chanhee Park, Sun Han, Jeongho Yoon et al.· 0 citations
Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and search remains unclear. Does RL create reasoning the base model lacks, or shift the rollout distribution toward trajectories it can already reach but rarely samples? We study this behaviorally with a Unified Decoding Framework (UDF), which expresses token-level sampling, beam-like search, tree search, and sequence-level resampling as executable policies over a shared budgeted operating space, scored post hoc with pass@$k$, self-consistency, best-of-$N$, and first-finish success. Using paired Base/RL checkpoints from SimpleRL-Zoo, we ask whether an RL default-policy curve can be approximated by a structured path of Base operating points. On Math500, AIME, GPQA, and IFEval, the pass@$k$ recovery path follows a Budgeted Operating-Point Transition Rule (BOPTR), $N_{\mathrm{Base}} \approx \alpha N_{\mathrm{RL}}^{\beta}$, with benchmark-conditioned exponents. On Qwen2.5-7B, BOPTR gives the lowest transfer error among the non-oracle rules we test, 3.41 pp (95% CI [2.32, 5.53]); a three-seed replication gives 3.07 $\pm$ 0.39 pp. The rule extends to ten models across four families (3.28 to 4.87 pp on checkpoints added after fitting), to four benchmarks it was never fitted on (5.03 pp vs. 4.44 pp in fit), and holds without an RL checkpoint for the target model (4.19 pp) or without RL supervision of any kind (5.08 pp). These results support a qualified internalized-search reading: under the recipe we test, much of the measured RL gain corresponds to a change in sampling efficiency toward operating points the base model can already reach under search. We treat the scaling patterns as descriptive of this recipe and cohort, report where they break down, and use UDF and BOPTR as behavioral diagnostics rather than evidence of parameter-level equivalence.
Wen-He Sun, Cun-Xiang Wang, Zijun Yao et al.· 0 citations
BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training and achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks.
Leichao Dong, Dong-Xu Zhang, Yi-Ding Sun et al.· arXiv.org· 0 citations
Inference-time search with large language models (LLMs) often concentrates on a small set of structurally or semantically similar trajectories, leaving alternatives underexplored---a failure mode we call \textit{reasoning basin collapse}. We introduce BASIN, a training-free, structure-aware selection method that groups reasoning states into basins and penalizes repeated visits to the same strategy, thereby reallocating search across genuinely distinct reasoning paths under a fixed compute budget. Under matched inference budgets, BASIN improves over Tree of Thoughts (ToT) by up to $+22$pp on Game of 24 and $+6.7$pp on MuSR. A quality-aware variant, QA-BASIN, further improves robustness by preserving high-quality basins when unconditional diversification over-explores. To explain when basin-aware selection helps, we introduce the redundancy gap $\Delta$, which measures how differently search concentrates for correct versus incorrect predictions: standard ToT often operates near $\Delta \approx 0$, while BASIN consistently shifts $\Delta$ positive. More broadly, BASIN suggests structure-aware selection as a simple and general approach to improving inference-time reasoning. Code can be found at https://github.com/GitHubLuCheng/basin.
This work proposes AutoVerifier, a residual-guided non-parametric optimization method that learns biases from recurring verifier errors and promotes them to code modules or prompt guidance only after replay validation detects no direct regressions, keeping accepted updates auditable, editable, and reusable.
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.
Lijie Yang, Hongyin Luo, Tri Dao et al.· 0 citations
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