122 Out-of-Distribution Generalisation with LSBD Representations (a) 0.5 (b) 0.625 (c) 0.75 (d) 0.875 Figure 5.11: 2D latent embeddings (top) and latent traversals (bottom) for LSBD-VAE trained on Arrow for increasingly large OOD splits, visualised on a flattened 2D torus. The embeddings colour map shows an ideal mapping if the pattern forms an axis-aligned grid. Embeddings of OOD data are shown in a lighter shade. 5.5 Conclusion This chapter investigates the out-of-distribution (OOD) generalisation of disentangled representations, in particular from the perspective of Linear SymmetryBased Disentanglement (LSBD). We reason why such representations should in theory generalise well to unseen (OOD) factor combinations, but in practice we observe that disentanglement models struggle to generalise well. We provide empirical results that showcase for which settings OOD generalisation seems to work, and where and how models fail. Overall our results imply that there is still work to be done to achieve OOD generalisation with disentangled models. The results, however, also show some promise that LSBD models can learn to express unseen factor combinations if there is sufficient coverage of combinations, although in practice decoders seem to struggle with correctly representing the unseen combinations even if their encodings satisfy equivariance quite well.
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