A Simple Strategy to Provable Invariance via Orbit Mapping

• URL: http://arxiv.org/abs/2209.11916v1
• Date: Sat, 24 Sep 2022 03:40:42 GMT
• Title: A Simple Strategy to Provable Invariance via Orbit Mapping
• Authors: Kanchana Vaishnavi Gandikota, Jonas Geiping, Zorah L\"ahner, Adam Czapli\'nski, Michael Moeller
• Abstract summary: We propose a method to make network architectures provably invariant with respect to group actions. In a nutshell, we intend to 'undo' any possible transformation before feeding the data into the actual network.
• Score: 14.127786615513978
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, 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. Further, we empirically analyze the properties of different approaches which incorporate invariance via training or architecture, and demonstrate the advantages of our method in terms of robustness and computational efficiency. 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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