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[bibtex]@InProceedings{Gandikota_2022_ACCV, author = {Gandikota, Kanchana Vaishnavi and Geiping, Jonas and L{\textasciidieresis}ahner, Zorah and ́ski, Adam Czaplin and \ensuremath{\ddot{}}oller, Michael M}, title = {A Simple Strategy to Provable Invariance via Orbit Mapping}, booktitle = {Proceedings of the Asian Conference on Computer Vision (ACCV)}, month = {December}, year = {2022}, pages = {3500-3518} }
A Simple Strategy to Provable Invariance via Orbit Mapping
Abstract
Many applications require robustness, or ideally invariance, of
a neural network to certain transformations of input data. Most commonly,
this requirement is addressed by either augmenting the training data, using
adversarial training, or defining network architectures that include the
desired invariance by design. In this work, we propose a method to make
network architectures provably invariant with respect to group actions by
choosing one element from a (possibly continuous) orbit based on a fixed
criterion. In a nutshell, we intend to 'undo' any possible transformation
before feeding the data into the actual network. We analyze properties of
such approaches, and demonstrate their advantages in terms of robustness
and computational efficiency in several numerical examples. In particular,
we investigate the robustness with respect to rotations of images (which
can hold up to discretization artifacts) as well as the provable orientation
and scaling invariance of 3D point cloud classification.
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