82 Quantifying and Learning Linear Symmetry-Based Disentanglement (LSBD) respectively 25%, 37.5%, and 12.5% of the data being involved in a labelled pair. Moreover, we see that with just a little supervision we outperform the best traditional method on DLSBD. Overall, these results suggest that with some expert knowledge (about the underlying group and a suitable representation) and limited annotation of transformations, LSBD can be achieved. 0 256 512 768 1024 1280 1536 1792 2048 Labeled pairs L 0.0 0.5 1.0 1.5 LSBD Square Dataset VAE 0 256 512 768 1024 1280 1536 1792 2048 Labeled pairs L 0.0 0.5 1.0 1.5 LSBD Arrow Dataset cc-VAE 0 256 512 768 1024 1280 1536 1792 2048 Labeled pairs L 0.0 0.5 1.0 1.5 LSBD Airplane Dataset DIP-VAE Figure 4.7: Box plots for DLSBD scores over 10 training repetitions for different numbers of labelled pairs L, for all datasets. The red line indicates the best-performing traditional disentanglement method. We only partially managed to reproduce the results from Quessard et al. (2020) on our datasets. Their method scored fairly well on the Airplane, ModelNet40, and COIL-100 datasets, but did not do well on the Square and Arrow dataset in our experiments. We highlight a particular case for the Arrow dataset, where the method clearly learns the rotations of the arrow but fails to learn colour. Figure 4.8
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