Learning low-dimensional representations that disentangle the underlying factors of variation in data has been posited as an important step towards interpretable machine learning with good generalization. To address the fact that there is no consensus on what disentanglement entails, Higgins et al. (2018) propose a formal definition for Linear Symmetry-Based Disentanglement, or LSBD, arguing that underlying real-world transformations give exploitable structure to data. Although several works focus on learning LSBD representations, none of them provide a metric to quantify disentanglement. Moreover, such methods require supervision on the underlying transformations for the entire dataset, and cannot deal with unlabeled data. We propose a metric to quantify LSBD representations that is easy to compute under certain well-defined assumptions. Furthermore, we present a method that can leverage unlabeled data, such that LSBD representations can be learned with limited supervision on transformations. Using our LSBD metric, our results show that limited supervision is indeed sufficient to learn LSBD representations.

提出了一种用于量化基于线性对称的解缠形式的度量 D_LSBD，进一步从这个度量推导出半监督的方法 LSBD-VAE 来学习 LSBD 表示，同时也表明多种期望性质均可通过 LSBD 表示实现。

基于线性对称性分离的量化和学习