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Many applications require robustness, or ideally invariance, of neuralnetworks to certain transformations of input data. Most commonly, thisrequirement is addressed by training data augmentation, using adversarialtraining, or defining network architectures that include the desired invarianceby design. In this work, we propose a method to make network architecturesprovably invariant with respect to group actions by choosing one element from a(possibly continuous) orbit based on a fixed criterion. In a nutshell, weintend to 'undo' any possible transformation before feeding the data into theactual network. Further, we empirically analyze the properties of differentapproaches which incorporate invariance via training or architecture, anddemonstrate the advantages of our method in terms of robustness andcomputational efficiency. In particular, we investigate the robustness withrespect to rotations of images (which can hold up to discretization artifacts)as well as the provable orientation and scaling invariance of 3D point cloudclassification.

A Simple Strategy to Provable Invariance via Orbit Mapping