发现推理越多越错的根源：模型对自己判断的不确定性越高时，额外推理会制造虚假信心。
Free Energy Heuristics: Fast-And-Frugal Cognition as Active Inference Under Uncertain Precision
- 用自由能最小化框架解释为何高不确定下推理反而有害
- 实验证明长链式推理在高不确定性任务上准确率下降17.3点
- 为快而简启发法与主动推断提供统一计算视角，适合认知科学与AI安全研究者
链式思维（CoT）能提升大语言模型在数学和符号推理中的表现，但在规划、伦理争议等无法自检的任务中，更多推理反而降低效果。本文提出，决定这一现象的关键是元不确定性——模型对自己证据可靠性的不确定程度。当元不确定性高时，额外推理不再增加信号，反而制造虚假自信。理论证明，在重尾精度先验下，最小化期望自由能的策略会在有限个高有效性线索后停止整合；在下降主导条件下，该策略与‘取最佳’启发法在样本层面完全一致。通过模拟与恢复相关性超0.96，构建了包含79个柯尼斯坦情境的基准集FEH-79，并对七种模型（五种开源3B-32B，两种前沿模型）进行预注册研究，共7875次响应。预设门限要求后验概率高于0.95且准确率下降超过6点，结果满足条件。高不确定性任务准确率下降17.3点（95%置信区间[7.7, 25.5]），而有确定答案的任务无损失。效应具有情景依赖性：在中大型模型中显著，在前沿模型中呈方向性，在最弱模型中则不显或反转。该框架揭示了何时CoT有效，并统一贝叶斯认知与快而简启发法传统：少即是多并非反对贝叶斯认知，而是元不确定性状态的证据。
原文摘要 · Abstract (English)
Chain-of-thought (CoT) improves large language models' performance in math and symbolic reasoning. But on planning, contested ethics, and tasks where the model cannot check itself, more reasoning makes things worse. Both effects are documented; what has been missing is a principled account of which property decides the outcome. We argue it is meta-uncertainty: how unsure the model is about the reliability of its own evidence. When that uncertainty is high, extra reasoning stops adding signal and starts manufacturing false confidence. We prove that the policy minimizing expected free energy under uncertain precision stops integrating cues after a finite number of high-validity ones when the precision prior is heavy-tailed (Theorem 2.6.1), and under a Descending Dominance condition, is sample-wise identical to take-the-best (Theorem 2.7.4). Fast-and-frugal heuristics and active inference are, then, two descriptions of the same computation. The prediction is that on high-meta-uncertainty items, longer CoT should degrade accuracy. We score the regime per item (simulate-and-recover rho > 0.96), build FEH-79, a benchmark of Knightian frames with matched controls, and run a pre-registered study across seven models (five open-weight 3B-32B, two frontier), five CoT lengths, and 7,875 responses. The gate, fixed before any data, required a negative interaction with posterior probability above 0.95 and an accuracy drop of more than 6 points. It held. The high-regime drop is 17.3 points (95% CI [7.7, 25.5]); matched items with definite answers show no cost. The effect is regime-dependent: decisive in capable mid-to-large models, directional in the two frontier systems, absent-to-reversed in the weakest. The framework answers when CoT helps and unifies the Bayesian and fast-and-frugal traditions: less-is-more effects are evidence about the meta-uncertainty regime, not against Bayesian cognition.
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