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.

本文将 DCI 框架连接到线性和非线性可识别性的两个概念，提出了一个具有两个新的表示质量度量的扩展 DCI-ES 框架，并指出了如何为黑盒预测器计算 D 和 C；我们的主要想法是使用表示所需的功能容量是表示质量中至关重要的但迄今被忽视的方面，我们 quantified therefore quantified 用明确性或易用性（E）；我们在 MPI3D 和 Cars3D 数据集上阐明了我们扩展的相关性。