论文标题
量化和学习基于线性对称性的分离
Quantifying and Learning Linear Symmetry-Based Disentanglement
论文作者
论文摘要
基于线性对称性的分解（LSBD）的定义正式化了线性分解表示的概念，但目前尚无量化LSBD的指标。这样的度量对于评估LSBD方法至关重要，并与先前对分解的理解进行比较。我们建议$ \ mathcal {d} _ \ mathrm {lsbd} $，一种数学上的声音指标，用于量化LSBD，并为$ \ mathrm {so}（so}（2）$组提供了实用实现。此外，从这个指标中，我们得出了LSBD-VAE，这是一种学习LSBD表示的半监督方法。我们通过证明（1）基于VAE的常见分离方法不学习LSBD表示，（2）LSBD-VAE以及其他最新方法可以学习LSBD表示，仅需要有限的监督，（3）由现有的分解计量表达的各种特性也可以实现LSBD，则证明了我们的指标的实用性。
The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the notion of linearly disentangled representations, but there is currently no metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and to compare to previous understandings of disentanglement. We propose $\mathcal{D}_\mathrm{LSBD}$, a mathematically sound metric to quantify LSBD, and provide a practical implementation for $\mathrm{SO}(2)$ groups. Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to learn LSBD representations. We demonstrate the utility of our metric by showing that (1) common VAE-based disentanglement methods don't learn LSBD representations, (2) LSBD-VAE as well as other recent methods can learn LSBD representations, needing only limited supervision on transformations, and (3) various desirable properties expressed by existing disentanglement metrics are also achieved by LSBD representations.
