In representation learning, a common approach is to seek representations which disentangle the underlying factors of variation. Eastwood & Williams (2018) proposed three metrics for quantifying the quality of such disentangled representations: disentanglement (D), completeness (C) and informativeness (I). In this work, we first connect this DCI framework to two common notions of linear and nonlinear identifiability, thereby establishing a formal link between disentanglement and the closely-related field of independent component analysis. We then propose an extended DCI-ES framework with two new measures of representation quality - explicitness (E) and size (S) - and point out how D and C can be computed for black-box predictors. Our main idea is that the functional capacity required to use a representation is an important but thus-far neglected aspect of representation quality, which we quantify using explicitness or ease-of-use (E). We illustrate the relevance of our extensions on the MPI3D and Cars3D datasets.

翻译：在表征学习中，一种常见方法是寻求解耦底层变化因子的表征。Eastwood和Williams（2018）提出了三个指标来量化此类解耦表征的质量：解耦度（D）、完备性（C）和信息性（I）。本文首先将这个DCI框架与两种常见的线性和非线性可辨识性概念建立联系，从而在解耦与密切相关的独立成分分析领域之间建立形式化关联。随后，我们提出了扩展的DCI-ES框架，引入两个新的表征质量度量——显式性（E）和规模（S），并指出如何针对黑盒预测器计算D和C。我们的核心思想在于：使用表征所需的功能容量是表征质量中重要但迄今被忽视的方面，我们通过显式性或易用性（E）来量化这一点。我们通过在MPI3D和Cars3D数据集上的实验验证了这些扩展的相关性。