Recent generative and tool-using AI systems can surface a large volume of candidates at low marginal cost, yet only a small fraction can be checked carefully. This creates a decoder-side bottleneck: downstream decision-makers must form reliable posteriors from many public records under scarce attention. We formalize this regime via Attention-Constrained Inference (ACI), in which a cheap screening stage processes $K$ records and an expensive verification stage can follow up on at most $B$ of them. Under Bayes log-loss, we study the maximum achievable reduction in posterior uncertainty per window, which we call \emph{epistemic throughput}. Our main result is a ``JaKoB'' scaling law showing that epistemic throughput has a baseline term that grows linearly with verification and prevalence, and an additional \emph{information-leverage} term that scales as $\sqrt{JKB}$, where $J$ summarizes screening quality. Thus, expanding cheap screening can nonlinearly amplify scarce verification, even when informative records are rare. We further show that this scaling is tight in a weak-screening limit, and that in the sparse-verification regime ($B \ll K$), substantial leverage requires heavy-tailed score distributions; for light-tailed scores the amplification is only logarithmic.

翻译：当前生成式与工具型人工智能系统能够以极低的边际成本生成大量候选结果，但其中仅有极小部分能被仔细核查。这形成了解码端的瓶颈：下游决策者必须在注意力稀缺的条件下，从海量公开记录中构建可靠的后验概率。我们通过注意力约束推断（ACI）框架对此机制进行形式化建模，其中廉价的筛选阶段处理$K$条记录，而昂贵的验证阶段最多能跟进其中$B$条。在贝叶斯对数损失下，我们研究每个时间窗口内可实现的后续不确定性最大缩减量，称之为\emph{认知通量}。我们的核心结论是呈现“JaKoB”缩放定律：认知通量包含随验证规模与事件发生率线性增长的基线项，以及按$\sqrt{JKB}$缩放（其中$J$表征筛选质量）的附加\emph{信息杠杆}项。因此，扩展廉价筛选能力可非线性放大稀缺验证资源的价值，即使有效信息记录本身较为罕见。我们进一步证明该缩放关系在弱筛选极限下是紧致的，且在稀疏验证机制（$B \ll K$）中，显著的信息杠杆效应要求得分分布具有重尾特性；对于轻尾得分分布，其放大效应仅为对数级。