潜在链式思维的能力与基本限制
Capabilities and Fundamental Limits of Latent Chain-of-Thought
AI总结：
本文提出潜在链式思维模型，揭示决策确定性对探索与执行的权衡影响，并通过理论分析和实验验证，证明课程学习在训练中的必要性。
摘要：
潜在链式思维（Latent CoT）模型通过连续表示实现高效的推理，但表现出令人困惑的性能不一致：在探索（ProsQA：97.0%）方面表现优异，但在计算（GSM8K：34.1%）方面却失败。我们揭示这种权衡由决策确定性所主导。我们的贡献有三方面：（1）我们理论上刻画了探索-执行权衡，证明高确定性使执行精确但抑制探索，而低确定性促进搜索但导致误差累积。（2）我们引入了符号索引——量化决策承诺——作为支配这种权衡的核心机制，并确立其与执行稳定性及探索能力之间的因果关系。（3）我们证明课程学习是理论上必要的，因为直接训练由于分布不匹配而注定失败。我们的框架将设计范式从二元架构选择转向适应性系统，使系统根据任务需求动态调节决策确定性。
英文摘要：
Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We reveal that this trade-off is governed by decisional certainty. Our contributions are threefold: (1) We theoretically characterize the fundamental Exploration-Execution Trade-off, proving that high certainty enables precise execution but inhibits exploration, while low certainty facilitates search but causes error accumulation. (2) We introduce the Symbolic Index--quantifying decisional commitment--as the core mechanism governing this trade-off and establish its causal relationship with both execution stability and exploration capability. (3) We prove that curriculum learning is theoretically necessary, as direct training provably fails due to distributional mismatch. Our framework shifts the design paradigm from binary architectural choices toward adaptive systems that dynamically regulate decisional certainty based on task demands.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
