Manufacturing lines, service journeys, supply chains, and AI reasoning chains share a common challenge: attributing a terminal outcome to the intermediate stage that caused it. We establish an information-theoretic barrier to this credit assignment problem: the signal connecting early steps to final outcomes decays exponentially with depth, creating a critical horizon beyond which reliable learning from endpoint data alone requires exponentially many samples. We prove four results. First, a Signal Decay Bound: sample complexity for attributing outcomes to early stages grows exponentially in the number of intervening steps. Second, Width Limits: parallel rollouts provide only logarithmic relief, with correlation capping the effective number of independent samples. Third, an Objective Mismatch: additive reward aggregation optimizes the wrong quantity when sequential validity requires all steps to be correct. Fourth, Optimal Inspection Design: uniform checkpoint spacing is minimax-optimal under homogeneous signal attenuation, while a greedy algorithm yields optimal non-uniform schedules under heterogeneous attenuation. Together, these results provide a common analytical foundation for inspection design in operations and supervision design in AI.

翻译：生产线、服务流程、供应链与人工智能推理链面临一个共同挑战：如何将终端结果归因于导致该结果的中间阶段。我们为此信用分配问题建立了一个信息论屏障：连接早期步骤与最终结果的信号会随深度呈指数级衰减，从而形成一个临界视界——超越此视界后，仅依靠端点数据进行可靠学习将需要指数级数量的样本。我们证明了四个结论。第一，信号衰减界限：将结果归因于早期阶段所需的样本复杂度随中间步骤数量呈指数增长。第二，宽度限制：并行推演仅能提供对数级缓解，相关性会限制有效独立样本数量。第三，目标失配：当序列有效性要求所有步骤均正确时，累加式奖励聚合会优化错误的目标量。第四，最优检查设计：在均匀信号衰减条件下，均匀检查点间距具有极小极大最优性；而在非均匀衰减条件下，贪心算法可产生最优的非均匀调度方案。这些结论共同为操作领域的检查设计与人工智能领域的监督设计提供了统一的分析基础。