76 Quantifying and Learning Linear Symmetry-Based Disentanglement (LSBD) (a) Square. (b) Arrow. (c) Airplane. Figure 4.5: Example paths of consecutive observations. focus on LSBD. In particular, we use disentanglement_lib (Locatello et al., 2018) to train a regular VAE (Kingma and Welling, 2013; Rezende et al., 2014), β-VAE (Higgins et al., 2017), cc-VAE (Burgess et al., 2018), FactorVAE (Kim and Mnih, 2018), and DIP-VAE-I/II (Kumar et al., 2017). We also include two weakly-supervised models, AdaGVAE and AdaMLVAE (Locatello et al., 2020), which are trained on pairs of data with few changing factors, to test whether this kind of supervision is helpful for LSBD. See Section 2.2 for more information on these traditional disentanglement models. Furthermore we evaluate the method from Quessard et al. (2020) that focuses on LSBD. We also tested Forward-VAE (Caselles-Dupré et al., 2019), but show only limited results since we were not able to reproduce any reasonable results for our datasets. Most of these methods have no notion of an underlying group structure, and thus do not give a fully fair comparison with our LSBD-VAE method. However, we emphasise that the main goal of our experiments is to investigate properties of disentangled representations from both the traditional and the LSBD perspective.
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