Generative networks are perfect tools to enhance the speed and precision of LHC simulations. It is important to understand their statistical precision, especially when generating events beyond the size of the training dataset. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is possible in specific regions of phase space, but not yet across the entire distribution.

翻译：生成网络是提升LHC模拟速度与精度的理想工具。理解其统计精度至关重要，尤其是在生成超出训练数据集规模的事件时。我们提出了两种互补的方法来估计放大因子，无需依赖大型保留数据集。平均放大法利用贝叶斯网络或集成学习，通过给定相空间体积上积分的精度来估计放大程度；微分放大法则采用假设检验来量化放大效应，且不损失任何分辨率。应用于最先进的事件生成器时，两种方法均表明在相空间的特定区域内可以实现放大，但尚未在整个分布范围内实现。