Double Machine Learning is often justified by nuisance-rate conditions, yet finite-sample reliability also depends on the conditioning of the orthogonal-score Jacobian. This conditioning is typically assumed rather than tracked. When residualized treatment variance is small, the Jacobian is ill-conditioned and small systematic nuisance errors can be amplified, so nominal confidence intervals may look precise yet systematically under-cover. Our main result is an exact identity for the cross-fitted PLR-DML estimator, with no Taylor approximation. From this identity, we derive a stochastic-order bound that separates oracle noise from a conditioning-amplified nuisance remainder and yields a sufficiency condition for root-n-inference. We further connect the amplification factor to semiparametric efficiency geometry via the Riesz representer and use a triangular-array framework to characterize regimes as residual treatment variation weakens. These results motivate an out-of-fold diagnostic that summarizes the implied amplification scale. We do not propose universal thresholds. Instead, we recommend reporting the diagnostic alongside cross-learner sensitivity summaries as a fragility assessment, illustrated in simulation and an empirical example.

翻译：双机器学习通常通过干扰率条件来论证其合理性，但有限样本的可靠性还取决于正交得分雅可比矩阵的条件数。这一条件数通常被假定而非被追踪。当残差化处理方差较小时，雅可比矩阵呈现病态，微小的系统性干扰误差可能被放大，导致名义置信区间看似精确却系统性覆盖不足。我们的主要结果是交叉拟合PLR-DML估计量的精确恒等式，无需泰勒近似。基于该恒等式，我们推导出一个随机阶界限，将理想噪声与条件数放大的干扰余项分离，并得到根号n推断的充分条件。我们进一步通过Riesz表示子将放大因子与半参数效率几何相关联，并利用三角阵列框架刻画残差处理变异减弱时的状态。这些结果启发了一种外折诊断方法，用于总结隐含的放大尺度。我们不提出普适阈值，而是建议在报告时将该诊断与跨学习器敏感性摘要并列，作为脆弱性评估，并通过仿真和实证案例加以说明。