Provable Adversarial Robustness for Group Equivariant Tasks: Graphs, Point Clouds, Molecules, and More
This work addresses a foundational gap in robust machine learning for geometric tasks, providing a sound framework for future research in robust and geometric ML.
The paper tackles the problem of defining and certifying adversarial robustness for tasks with inherent equivariances, such as rotation or permutation, by proposing a new robustness notion and developing equivariance-preserving randomized smoothing for architecture-agnostic certification, achieving provable guarantees for tasks like node classification.
A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance. We then demonstrate that provable robustness can be achieved by (1) choosing a model that matches the task's equivariances (2) certifying traditional adversarial robustness. Certification methods are, however, unavailable for many models, such as those with continuous equivariances. We close this gap by developing the framework of equivariance-preserving randomized smoothing, which enables architecture-agnostic certification. We additionally derive the first architecture-specific graph edit distance certificates, i.e. sound robustness guarantees for isomorphism equivariant tasks like node classification. Overall, a sound notion of robustness is an important prerequisite for future work at the intersection of robust and geometric machine learning.