这篇论文提出了一个量化框架，告诉你什么时候该在推理中增加中间步骤，什么时候不该。有具体数据支撑，适合做推理优化的研究参考。
论文提出约束路径推理（CPR）框架，通过源感知路径假设和阶段级核算来评估LLM推理中中间承诺阶段的价值。在1,180个生成的QCQP和40个工程退化多项式实例（2,140个端点）上，残差分类恢复63.0%的修复全部额外可行产出，仅用17.7%的尝试。固定LLM核算（270次唯一调用）显示可行产出率：直接41.1%，形式化与确定性执行后90.0%，一次凸化后20.0%，完整路径21.1%。在120次配对条件调用中，两步回滚规则达到90%可行产出，而反馈条件选择器仅为36.7%。
Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost
When does a committed intermediate stage in an LLM reasoning pipeline earn its cost? Constrained Path Reasoning (CPR) pairs a source-aware path hypothesis with stage-level accounting. Search generates provisional states; trusted or validated invariants can constrain hard, while other proposals remain soft and revisable. CPR predicts that task-compatible commitments can factor transitions, concentrate candidate mass, induce regularity, and expose feedback when their gains exceed propagated error and execution cost. The formalism covers discrete commitments and continuous flows and measures effective branching, endpoint concentration, and cost per usable output. Across 1,180 generated QCQPs and 40 engineered degenerate polynomial instances (2,140 endpoints), residual triage recovers 63.0% of repair-all's additional feasible yield with 17.7% of its attempts. Fixed-LLM accounting (270 unique calls shared across nested arms) finds usable yield of 41.1% direct, 90.0% after formalization and deterministic execution, 20.0% after one-shot convexification, and 21.1% for the full path. In 120 paired-condition calls, a two-action rollback rule reaches 90% usable yield versus 36.7% for the feedback-conditioned selector. Two endpoint probes separate source from validation: a 72-output cross-trajectory transplant reduces entropy and acceptable mass; a 24-output same-call self-proposal pilot gives unchanged two-repeat collision entropy, 25.0% versus 8.3% usable yield, and 1/8 deterministically confirmed endpoint checks. Model-generated states supply hypotheses; trusted execution earns constraint strength.