The ability of Variational Autoencoders to learn disentangled representations has made them appealing for practical applications. However, their mean representations, which are generally used for downstream tasks, have recently been shown to be more correlated than their sampled counterpart, on which disentanglement is usually measured. In this paper, we refine this observation through the lens of selective posterior collapse, which states that only a subset of the learned representations, the active variables, is encoding useful information while the rest (the passive variables) is discarded. We first extend the existing definition to multiple data examples and show that active variables are equally disentangled in mean and sampled representations. Based on this extension and the pre-trained models from disentanglement lib, we then isolate the passive variables and show that they are responsible for the discrepancies between mean and sampled representations. Specifically, passive variables exhibit high correlation scores with other variables in mean representations while being fully uncorrelated in sampled ones. We thus conclude that despite what their higher correlation might suggest, mean representations are still good candidates for downstream tasks applications. However, it may be beneficial to remove their passive variables, especially when used with models sensitive to correlated features.

翻译：变分自编码器学习解耦表示的能力使其在实践应用中备受青睐。然而，近期研究表明，通常用于下游任务的均值表示比用于衡量解耦性的采样表示具有更强的相关性。本文通过选择性后验坍缩的视角深化这一观察——该理论指出，仅有部分学习到的表示（即活跃变量）编码有用信息，而其余部分（被动变量）被丢弃。我们首先将现有定义扩展至多数据样本场景，并证明活跃变量在均值表示和采样表示中具有同等的解耦性。基于这一扩展及disentanglement lib的预训练模型，我们继而分离出被动变量，揭示其正是导致均值与采样表示差异的根源。具体而言，被动变量在均值表示中与其他变量呈高度相关，而在采样表示中则完全无相关。因此我们得出结论：尽管均值表示呈现更高相关性，其仍适用于下游任务应用；但去除被动变量可能更为有益，尤其当模型对特征相关性敏感时。