In this work, we unify several expected generalization error bounds based on random subsets using the framework developed by Hellstr\"om and Durisi [1]. First, we recover the bounds based on the individual sample mutual information from Bu et al. [2] and on a random subset of the dataset from Negrea et al. [3]. Then, we introduce their new, analogous bounds in the randomized subsample setting from Steinke and Zakynthinou [4], and we identify some limitations of the framework. Finally, we extend the bounds from Haghifam et al. [5] for Langevin dynamics to stochastic gradient Langevin dynamics and we refine them for loss functions with potentially large gradient norms.

翻译：在这项工作中,我们利用由Hellstr\'om和Durisi[1]制定的框架,根据随机子集,统一了若干预期的一般性错误界限。首先,我们从Bu等人[2] 和Negrea等人[3] 收集单个样本相互信息[2] 和数据集的一个随机子集,收回了这些界限。然后,我们在Steinke和Zakynthinou[4] 的随机分集设置中引入了新的类似界限,我们确定了框架的一些局限性。最后,我们将Langevin动态从Haghifam等人[5] 的范围扩大到了随机梯度梯度兰格文动态,我们用潜在的大梯度规范来完善了这些界限,用于损失功能。