4.6 Experimental Setup 77 4.6.5 Disentanglement Metrics We use encodings from all methods to evaluate DLSBD, as well as common traditional disentanglement metrics fromdisentanglement_lib: Beta (Higgins et al., 2017), Factor (Kim and Mnih, 2018), SAP (Kumar et al., 2017), DCI Disentanglement (Eastwood and Williams, 2018), Mutual Information Gap (MIG) (Chen et al., 2018), and Modularity (MOD) (Ridgeway and Mozer, 2018). See Section 2.2 for a brief explanation of each of these metrics. 4.6.6 Further Experimental Details We now provide some more information about the architectures, epochs, and hyperparameters for our experiments. For the traditional disentanglement methods trained on Square, Arrow and Airplane datasets the latent spaces have 4 dimensions, since these are the minimum number of dimensions necessary to learn LSBD representations for an underlying SO(2) ×SO(2) symmetry group (Higgins et al., 2018; Caselles-Dupré et al., 2019). For COIL-100 and ModelNet40 we use latent spaces with 7 dimensions for a fair comparison with the LSBD-VAE method. Architectures Table 4.1 shows the encoder and decoder architectures used for almost all methods and datasets. The encoder’s last layer depends on the method. For VAE, cc-VAE, FactorVAE, DIP-I, DIP-II, we used two dense layers with 4 units each. For LSBD-VAE and ∆VAE we used two dense layers with 4 and 2 units each. For Quessard we used a single dense layer with 4 units. The only model that was not trained with this architecture was LSBD-VAE/0 method for the ModelNet40 dataset, since during training the loss was getting NaN values. In this case we used the architecture from Table 4.2. Hyperparameters Table 4.3 shows the hyperparameters used to train the LSBD-VAE models for each dataset. Table 4.4 shows the hyperparameters used to train the other models for all datasets. We increased the range of values for the scale parameter t for ModelNet40 and COIL-100, since we noticed that this provided better results in terms of data reconstruction and disentanglement. For the Arrow dataset, a value of γ = 1 was producing unstable results. However, the values 10, 100,
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