突破马尔可夫诅咒：基于非对称认知潜能的多智能体辩论
Breaking the Martingale Curse: Multi-Agent Debate via Asymmetric Cognitive Potential Energy
AI总结：
AceMAD通过非对称认知潜能打破马尔可夫诅咒，提升多智能体辩论的真理收敛能力。
摘要：
多智能体辩论（MAD）已发展为增强大语言模型推理的一种有前途的范式。然而，近期的研究揭示了一个局限性：标准的MAD无法在多数投票之上提升信念正确性；我们将其称为马尔可夫诅咒。这种诅咒的出现是因为相关误差导致智能体趋向于错误的一致性，其中辩论仅仅是强化集体错误而非过滤噪声。我们提出了AceMAD框架，通过利用非对称认知潜能将MAD从随机游走转变为具有正漂移的定向收敛过程。通过同伴预测机制，智能体预测其同伴的信念分布，揭示出非对称认知潜能：真理持有者不仅知道正确答案，而且预见到大众的误解，而幻觉多数则对集体错误毫无察觉。这种非对称性创造了一个潜在的能量差距，我们通过严格恰当评分规则进行量化。我们证明这种认知潜能表现为信息论上的优势，并且在非线性聚合下转化为向真理的子随机游走漂移，直接突破马尔可夫诅咒。在六个基准测试的挑战子集上进行的实验表明，AceMAD即使在初始多数错误的情况下也能恢复稀疏的真理信号，显著优于基线方法。
英文摘要：
Multi-Agent Debate (MAD) has emerged as a promising paradigm for enhancing large language model reasoning. However, recent work reveals a limitation:standard MAD cannot improve belief correctness beyond majority voting; we refer to this as the Martingale Curse. This curse arises because correlated errors cause agents to converge toward erroneous consensus, where debate merely reinforces collective mistakes rather than filtering noise. We propose AceMAD, a framework that breaks the Martingale Curse by harnessing asymmetric cognitive potential energy to transform MAD from a random walk into a directed convergence process with positive drift. Through a peer-prediction mechanism, agents predict their peers' belief distributions, revealing asymmetric cognitive potential: truth-holders not only know the correct answer but also anticipate the crowd's misconceptions, while the hallucinating majority remains blind to their collective error. This asymmetry creates a potential energy gap that we quantify via strictly proper scoring rules. We prove this cognitive potential manifests as information-theoretic superiority and, under nonlinear aggregation, converts into submartingale drift toward truth, directly breaking the Martingale Curse. Experiments on challenging subsets across six benchmarks show AceMAD recovers sparse truth signals even when initial majorities are incorrect, substantially outperforming baseline methods.
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