A Simple Strategy to Provable Invariance via Orbit Mapping
This addresses the need for reliable invariance in neural networks for applications like image and point cloud classification, offering a provable solution that is incremental over existing methods.
The paper tackles the problem of ensuring neural network invariance to transformations like rotations and scaling by proposing a method to provably select a canonical element from an orbit before processing, achieving robustness and computational efficiency in image and 3D point cloud tasks.
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.