Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost

Reasoning traces of large language models are widely read as containing "breakthrough" moments and early-legible fates. Both readings rest on measurements missing a counterfactual control at the level of the claim; we supply both controls. First, a restart-controlled truncation probe separates when a solution fits the continuation budget from when a prefix carries value that fresh computation cannot buy, comparing per-anchor continuation solve rates against from-scratch restart curves at matched total generated-token budget. Applied to 178 problem-model cells (89 MATH problems x two small open models, an outcome-blind but difficulty-targeted cohort), exactly 1 of 178 cells survives as prefix-limited; restart dose-response separates a compute-starved model from a capability-limited one; and wherever the matched budget lies inside the restart grid, continuing the model's own prefix beats restarting (9 of 9) -- predominantly compute compression rather than expanded reachability. Second, a pre-registered, difficulty-controlled test finds no detectable outcome information in early-window internal signals beyond a problem-difficulty baseline, and two generation-free analyses of public corpora show why this control is needed: a trace-blind difficulty proxy reaches AUROC 0.873 on 192K DeepSeek-R1 generations -- inside the published probe range -- and a closely matched reconstruction of the closest published early-window positive recovers a comparable pooled result (0.849) while within problem it is statistically indistinguishable from chance at all ten anchors (0.496 at t=4); a post-hoc within-targeted probe finds only a small average residual, concentrated in three low-failure problems. High pooled probe AUROCs cannot by themselves establish within-attempt information; a question-only baseline or within-problem evaluation is required.

We independently reproduce two recent methods for making large language model (LLM) reasoning more reliable, and stress-test them across domains and models (RPC across four new task domains with Qwen3-8B, LCF across four 7-8B models). The first, RPC, aggregates token probabilities and self-consistency at inference; the second, LCF, trains projectors that split hidden states into "content" and "logic" and edits the logic part toward a valid region. Validating such reliability claims matters because the original evaluations are run by each method's own authors and were never independently reproduced or stress-tested across models and domains, and LCF shipped no public code. We re-run RPC's published-path aggregation and re-implement LCF's projector, contrastive, and intervention pipeline, then extend both to text-to-SQL, legal extraction, fallacy identification, and precedent grading, and probe LCF's representation directly. RPC reproduces the original grid exactly on the authors' released reasoning paths; on four new domains its edge over self-consistency is never significant (ties or small mixed differences, paired p >= 0.28), and on BIRD, the one domain where we vary the budget, the edge grows with K as predicted but its largest gap (+2.5 accuracy at K=32, p=0.16) reverses to -0.25 when we enlarge the sample to n=200. LCF's logic-validity direction is real but weak (0.82 separability at the single best sub-layer versus 0.95 for a semantic-attribute control); its one positive effect (Qwen3 $Δ$Prob) is not significant (p=0.56), while it significantly reduces $Δ$Prob on two of the other three models.

Parallel reasoning enhances Large Reasoning Models (LRMs) but incurs prohibitive costs due to futile paths caused by early errors. To mitigate this, path pruning at the prefix level is essential, yet existing research remains fragmented without a standardized framework. In this work, we propose the first systematic taxonomy of path pruning, categorizing methods by their signal source (internal vs. external) and learnability (learnable vs. non-learnable). This classification reveals the unexplored potential of learnable internal methods, motivating our proposal of STOP (Super TOken for Pruning). Extensive evaluations across LRMs ranging from 1.5B to 20B parameters demonstrate that STOP achieves superior effectiveness and efficiency compared to existing baselines. Furthermore, we rigorously validate the scalability of STOP under varying compute budgets - for instance, boosting GPT-OSS-20B accuracy on AIME25 from 84% to nearly 90% under fixed compute budgets. Finally, we distill our findings into formalized empirical guidelines to facilitate optimal real-world deployment. Code, data and models are available at https://bijiaxihh.github.io/STOP