多组件 LLM 代理从每个组件仅看到联合问题的一部分; 中组装概率声明，即使每个组件都是局部一致的，该组合也可能违反基本概率公理。我们通过组合残差 eps*, 形式化这种局部相干, 全局不相干故障，即从组合引用到运行时可根据系统输出和声明的跨组件耦合约束计算的联合相干多胞体, 的 L2 距离。当局部一致性满足,并且瑞利商预测在四个关系类中的三个上与观察到的残差在7%内匹配时，产品结构二分法表征。分层 Boyle-Dykstra 投影可确定性地修复成分; 任何时间有效的电子流程可提供顺序相干性监控。在四名 LLM 中级面板上的 1,876 整体派系 ( 前沿面板在第 5.5), eps 中重新运行* > 0 在 33-94% 派系, 上，转换为 +0.115 纳特，在比例分配规则下，在 1,770 解决的投注上每注后悔投注(在投注者自身连贯性)的情况下，收益会暴跌至+0.006。三个直观的 LLM 端缓解(检索, 分区感知提示, 聚合器-LLM) 均失败或回归。
Multi-component LLM agents assemble probabilistic claims from components that each see only part of a joint problem; the composition can violate basic probability axioms even when every component is locally coherent. We formalise this locally coherent, globally incoherent failure via the compositional residual eps*, the L2 distance from the composed quote to the joint coherent polytope, computable at runtime from system output and the declared cross-component coupling constraints. A product-structure dichotomy characterises when local coherence suffices, and a Rayleigh-quotient prediction matches the observed residual within 7% on three of four relation classes. A hierarchical Boyle-Dykstra projection repairs the composition deterministically; an anytime-valid e-process gives sequential coherence monitoring. Across 1,876 ensemble cliques on a four-LLM mid-tier panel (frontier-panel rerun in Section 5.5), eps* > 0 on 33-94% of cliques, translating to +0.115 nats per bet of regret on 1,770 resolved bets under the proportional allocation rule (the gain collapses to +0.006 under bettors that themselves coherentise). Three intuitive LLM-side mitigations(retrieval, partition-aware prompting, aggregator-LLM) each fail or regress.
科目: 人工智能 (cs.AI); 计算和语言 (cs.CL)
Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL)