CoT有效与否取决于推理步骤间的转移一致性。
When does Chain-of-Thought Help: A Markovian Perspective
- 将推理过程建模为马尔可夫链，分析每步转移的相似性
- 相同转移模式下，CoT能显著降低所需样本数
- 适合研究推理机制或设计更优提示策略的人
Chain-of-Thought（CoT）提示是提升模型推理能力的常用方法，但其效果在不同任务间差异明显。本文从马尔可夫视角分析其有效性：将推理的每一步视为状态，步骤间的依赖由转移核描述。理论表明，若不同实例具有相同的逐步转移核，即转移对齐，则CoT能降低推理时的样本复杂度——更少的上下文轨迹即可恢复最终决策。反之，若转移不一致，优势可能消失。此外，我们量化了中间步骤噪声对CoT收益的影响。为验证理论，设计了可分离关键因素的合成基准，补充真实任务上的已有结果，实证支持预测。
原文摘要 · Abstract (English)
Chain-of-Thought (CoT) prompting is a widely used inference-time technique for improving reasoning, yet its gains are uneven across tasks. We analyze when and why CoT helps by modeling the step-wise reasoning trajectory as a Markov chain. Each intermediate step is a state and the dependence between steps is captured by a transition kernel. Our theory identifies transition alignment, whether instances share a common step-wise transition kernel, as the key determinant of CoT's effectiveness. When transitions are identical across steps, CoT reduces inference-time sample complexity: fewer context sample trajectories suffice to recover the final decision. In contrast, when transitions differ across steps, these gains can vanish. We further quantify how noise in intermediate steps modulates CoT's benefit. Beyond theory, we design synthetic benchmarks that isolate these factors to complement prior results on real-world tasks and to empirically validate our predictions.
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