Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks remains mostly unanswered despite their strong ability for sample generation and density estimation. This paper investigates this problem for such a family of generative models that admits exact invertibility. We propose Neural Principal Component Analysis (Neural-PCA) that operates in full dimensionality while capturing principal components in \emph{descending} order. Without exploiting any label information, the principal components recovered store the most informative elements in their \emph{leading} dimensions and leave the negligible in the \emph{trailing} ones, allowing for clear performance improvements of $5\%$-$10\%$ in downstream tasks. Such improvements are empirically found consistent irrespective of the number of latent trailing dimensions dropped. Our work suggests that necessary inductive bias be introduced into generative modelling when representation quality is of interest.

该研究旨在通过无监督生成学习探索有用的表示方法，对比发现现有的正则流是否对下游任务提供有效的表示方法。作者提出了神经主成分分析方法(即 Neural-PCA) ，该方法以完整维度为操作对象捕获主成分并在其中按下降顺序进行排序，利用该方法可以得到表现明显优于(5%至10%)其他方法的结果。此项工作指出，在关注表示质量时，必须引入必要的归纳偏见，从而提高下游任务的性能。

基于流形表征学习的神经PCA