发表机构
Université Paris 1; Faculty of Science and Technology of Tangier; Abdelmalek Essaadi University（巴黎第一大学; 丹吉尔科学与技术学院; 阿卜杜勒马利克·埃萨迪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示变换审计中配对计数高估覆盖率的问题，提出四个互补度量并推导精确留一轨道更新及源不相交部署门，以提升审计可靠性与部署安全性。
AI 中文摘要
计数等价对是报告变换审计覆盖率的常见方式，但它可能大幅夸大审计所施加的约束：从同一语义对象生成的配对是相关的，且完整轨道图包含代数冗余边。因此，我们区分四个互补的量——边数 $m$、有效对比秩 $s$、总体支持秩 $r$ 和图谱间隙 $\eta$——并刻画它们在审计覆盖率和部署可靠性中的作用。在秩为 $r$ 的高斯对比模型下，当且仅当锚点在 $\ker T$ 中有分量时，存在总体不变的校准读取器。当审计的秩 $s < r$ 时，其未观测风险为 $R^\star/U$，其中 $U \sim \operatorname{Beta}((r-s)/2,s/2)$；当 $s \ge r$ 时，精确校准插值不可行。同样的区别出现在轨道拓扑中：生成树施加与完全图相同的精确零约束，而尖锐的图庞加莱不等式以与 $1/\eta$ 成比例的成本将边级漂移传播到整个轨道。循环审计还可以在不排除任何语义对象的情况下产生零配对级留一误差。为解决这些失败，我们推导了精确的块伍德伯里留一轨道更新，并在有限个候选读取器上引入源不相交的部署门。该门保留原始读取器，除非不确定性界限在规定的清洁效用预算内证明更低的漂移。
英文摘要
Counting equivalent pairs is a common way to report transformation-audit coverage, but it can substantially overstate the constraints imposed by an audit: pairs generated from the same semantic object are correlated, and complete orbit graphs contain algebraically redundant edges. We therefore distinguish four complementary quantities---edge count $m$, effective contrast rank $s$, population support rank $r$, and graph spectral gap $η$---and characterize their roles in audit coverage and deployment reliability. Under a rank-$r$ Gaussian contrast model, a population-invariant calibrated reader exists exactly when the anchor has a component in $\ker T$. When an audit has rank $s < r$, its unobserved risk is $R^\star/U$, with $U \sim \operatorname{Beta}((r-s)/2,s/2)$; when $s \ge r$, exact calibrated interpolation is infeasible. The same distinction appears in orbit topology: a spanning tree imposes the same exact-null constraints as a complete graph, while a sharp graph Poincare inequality propagates edge-level drift to an entire orbit at a cost proportional to $1/η$. Cyclic audits can additionally yield zero pair-level leave-one-out error without holding out any semantic object. To address these failures, we derive exact block-Woodbury leave-one-orbit-out updates and introduce a source-disjoint deployment gate over finitely many candidate readers. The gate retains the original reader unless uncertainty bounds certify lower drift within a prescribed clean-utility budget. etc..
Comments15 pages, 3 figures
