Training or Architecture? How to Incorporate Invariance in Neural Networks

TL;DR

This paper introduces a method for creating neural networks that are provably invariant to transformations like rotations and scaling by selecting a representative from each transformation orbit, enhancing robustness and efficiency.

Contribution

The authors propose a novel approach to achieve provable invariance in neural networks by choosing a representative element from the transformation orbit, applicable to continuous groups.

Findings

Demonstrated robustness to image rotations with discretization artifacts

Achieved provable rotational and scaling invariance in 3D point cloud classification

Improved computational efficiency over traditional invariance methods

Abstract

Many applications require the robustness, or ideally the 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 automatically. Unfortunately, the latter often relies on the ability to enlist all possible transformations, which make such approaches largely infeasible for infinite sets of transformations, such as arbitrary rotations or scaling. In this work, we propose a method for provably invariant network architectures 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, extend them to equivariant networks, and demonstrate their advantages in terms of robustness as well as computational efficiency in several numerical examples. In particular, we investigate the robustness with respect to rotations of images (which can possibly hold up to discretization artifacts only) as well as the provable rotational and scaling invariance of 3D point cloud classification.