让AI解题前先抓约束条件，避免答错格式或数值。
Constraint-First Reasoning: A Training-Free Protocol for Exploiting Answer-Space Constraints in Mathematical Problem Solving
- 先提取题目隐含的限制条件，再解题时逐步核对。
- 在多个数学竞赛数据集上超越传统链式思考方法。
- 适合需要严格格式和数值准确的数学推理任务。
大型语言模型虽能推导出合理数学解，但仍可能违反明确要求，如遗漏模运算、返回非整数或使用错误答案格式。本文提出无需训练的两阶段提示协议——约束优先推理（CFR）：第一阶段提取并总结题目蕴含的约束条件；第二阶段求解时持续校验中间与最终结果是否符合该总结。路由式CFR仅在检测到特定限制性线索时启用两阶段流程，否则采用直接链式思考（CoT）。在AIME、CMIMC、BRUMO和AIMO_AMC等多个数据集上，该方法在多种基线模型上均优于直接CoT。通过对照实验、配对测试、解码鲁棒性分析、约束质量审计、总词元统计及OlympiadBench评估，表明CFR是一种针对特定场景的测试时干预手段，其效果依赖于可恢复的约束条件与可靠的第一阶段提取能力，而非通用数学推理替代方案。
原文摘要 · Abstract (English)
Large language models can derive a plausible mathematical object yet still violate explicit requirements--for example, by omitting a modular reduction, returning a non-integer, or using the wrong encoded answer form. We introduce Constraint-First Reasoning (CFR), a training-free two-stage prompting protocol: Stage 1 extracts and summarizes constraints entailed by the problem, and Stage 2 solves while checking intermediate and final results against that summary. Routed-CFR activates the two-stage protocol only when a text-only regex router detects restrictive cues; otherwise it uses direct chain-of-thought (CoT). Across AIME, CMIMC, BRUMO, and AIMO_AMC, the method improves direct CoT on multiple backbones. We further report convention-controlled routing experiments, matched prompting baselines, problem-level paired tests, decoding robustness, constraint-quality audits, total-token accounting, and an OlympiadBench evaluation. These analyses position CFR as a targeted test-time intervention whose benefit depends on recoverable constraints and reliable Stage 1 extraction, rather than as a general-purpose replacement for mathematical reasoning.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。