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Many machine learning techniques incorporate identity-preservingtransformations into their models to generalize their performance to previouslyunseen data. These transformations are typically selected from a set offunctions that are known to maintain the identity of an input when applied(e.g., rotation, translation, flipping, and scaling). However, there are manynatural variations that cannot be labeled for supervision or defined throughexamination of the data. As suggested by the manifold hypothesis, many of thesenatural variations live on or near a low-dimensional, nonlinear manifold.Several techniques represent manifold variations through a set of learned Liegroup operators that define directions of motion on the manifold. However,these approaches are limited because they require transformation labels whentraining their models and they lack a method for determining which regions ofthe manifold are appropriate for applying each specific operator. We addressthese limitations by introducing a learning strategy that does not requiretransformation labels and developing a method that learns the local regionswhere each operator is likely to be used while preserving the identity ofinputs. Experiments on MNIST and Fashion MNIST highlight our model's ability tolearn identity-preserving transformations on multi-class datasets.Additionally, we train on CelebA to showcase our model's ability to learnsemantically meaningful transformations on complex datasets in an unsupervisedmanner.

Learning Identity-Preserving Transformations on Data Manifolds