CONTENTS xiii 4.7.1 Standard Disentanglement Methods Don’t Learn LSBD Representations.......................... 80 4.7.2 LSBD-VAE and other LSBD Methods Can Learn LSBD Representations with Limited Supervision on Transformations 81 4.7.3 LSBD Representations Also Satisfy Previous DisentanglementNotions......................... 83 4.7.4 Full Quantitative Results . . . . . . . . . . . . . . . . . . . 85 4.7.5 Further Qualitative Results . . . . . . . . . . . . . . . . . 89 4.8 SHREC 2021 Object Retrieval Challenge . . . . . . . . . . . . . . 93 4.8.1 TheChallenge ........................ 94 4.8.2 OurMethodology....................... 95 4.8.3 ResultsandConclusions . . . . . . . . . . . . . . . . . . . 99 4.9 Conclusion ..............................103 5 Out-of-Distribution Generalisation with LSBD Representations 105 5.1 Introduction..............................106 5.2 RelatedWork .............................108 5.3 ExperimentalSetup..........................110 5.3.1 Datasets............................110 5.3.2 OOD Splits: Left-out Factor Combinations . . . . . . . . . 111 5.3.3 LSBD-VAE...........................112 5.3.4 Traditional Disentanglement Models . . . . . . . . . . . . 114 5.4 ExperimentsandResults.......................115 5.4.1 Likelihood Ratio: Training vs. OOD ELBO . . . . . . . . . 115 5.4.2 OOD Detection: Area Under ROC Curve (AUROC) . . . . 117 5.4.3 Reconstructions of OOD Combinations . . . . . . . . . . . 119 5.4.4 Equivariance of OOD Combinations . . . . . . . . . . . . . 120 5.5 Conclusion ..............................122 6 Conclusion and Future Work 123 6.1 Conclusions ..............................123 6.2 Limitations ..............................125 6.3 FutureWork..............................128 Bibliography 131 Curriculum Vitae 141 Acknowledgements 143
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