大模型多步推理易陷入思维陷阱，导致推理质量下降却误保答案正确。
The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning
- 用信息论证明多智能体辩论会弱化推理依据，而非提升多样性。
- 在科学事实数据集上，推理可信度下降43%，多数投票机制几乎丢尽可信度。
- 提出基于证据的苏格拉底式追问，可恢复98%的推理可信度，适合改进AI可解释性。
当同一语言模型被多次提示进行辩论时，其输出呈现单一视角的不同表述，而非多元观点。多智能体辩论（MAD）及更广泛的封闭系统推理中，尽管答案准确率得以保持，但推理过程的质量持续退化。我们称此现象为‘辩论陷阱’与‘推理陷阱’，并提出一套以证据为基础的推理失败理论框架。该框架包含三部分：(i) SFS（支持忠实度评分），用于验证分解后原子命题与证据的一致性（分解器无关排序：斯皮尔曼相关系数=1.0）；(ii) EGSR（证据基础苏格拉底推理），以证据驱动的提问替代对抗性论证；(iii) 定理1（DPI界）：在标准MAD下，链式结构E→O⁰→O¹→…满足马尔可夫性，数据处理不等式表明期望信息量递减，即E[I(E;O^{t+1})] ≤ E[I(E;O^t)]。配套结果包括开放系统恢复（定理2）、EGSR累积效应（引理2）与投票聚合下限（命题1），将多步推理按其与证据的信息关系分类。在SciFact（300个主张）和FEVER（1000个主张）共16种条件下，DebateCV（C13）保留88%基准准确率，但SFS下降43%；多数投票的MAD（C15）使SFS降至基线的1.7%（p < 10⁻⁶，d = -0.96）；EGSR则恢复至98%。一项包含韩语10×30和英语3×200样本的群体研究发现，跨评估者一致性（Fleiss kappa）≤ +0.018，且领域与语言间评分者内部一致性波动为0.8–1.4，表明用于校准忠实度指标的人类共识本身并不稳定。我们提出一个可检验猜想：任何维持定理1马尔可夫结构的封闭系统推理协议，在期望上都受相同DPI界约束。
原文摘要 · Abstract (English)
When copies of the same language model are prompted to debate, they produce diverse phrasings of one perspective rather than diverse perspectives. Multi-agent debate (MAD), and more broadly closed-system reasoning where agents iteratively transform each other's outputs, tends to preserve answer accuracy while degrading the reasoning behind those answers. We name the multi-agent case the Debate Trap and the broader phenomenon the Reasoning Trap, offering a programmatic theory of evidence-grounded reasoning failure.The framework has three parts: (i) SFS (Supported Faithfulness Score), a claim-level metric verifying decomposed atomic claims against provided evidence (decomposer-invariant rankings: Spearman rho=1.0); (ii) EGSR (Evidence-Grounded Socratic Reasoning), replacing adversarial argumentation with evidence-grounded inquiry; (iii) Theorem 1 (DPI Bound): under standard MAD, the chain E -> O^0 -> O^1 -> ... is Markov, and the Data Processing Inequality implies E[I(E;O^{t+1})] <= E[I(E;O^t)]. Three companion results -- open-system recovery (Theorem 2), EGSR accumulation (Lemma 2), and vote-aggregation floor (Proposition 1) -- partition multi-step LLM reasoning by its information-theoretic relationship to E. Across 16 conditions on SciFact (300 claims) and FEVER (1,000 claims), DebateCV (C13) preserves 88% of baseline accuracy while SFS drops 43%; majority-vote MAD (C15) reduces SFS to 1.7% of baseline (p < 10^{-6}, d = -0.96); EGSR recovers 98%. An R6 cohort study (Korean n=10x30 FEVER; English n=3x200 SciFact) finds inter-rater Fleiss kappa <= +0.018 with 0.8-1.4 Likert intra-rater shifts across language and domain -- the human agreement that faithfulness metrics have been calibrated against is not itself stable. We offer one falsifiable conjecture: any closed-system reasoning protocol preserving Theorem 1's Markov structure is, in expectation, subject to the same DPI bound.
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