# Provable Adversarial Robustness for Group Equivariant Tasks: Graphs, Point Clouds, Molecules, and More

arXiv: https://arxiv.org/abs/2312.02708 · HTML: https://mlsanity.com/paper/2312.02708/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2023.

## Built on by (most cited first, 3 of 3)

- [Soft Prompt Threats: Attacking Safety Alignment and Unlearning in Open-Source LLMs through the Embedding Space](https://mlsanity.com/paper/2402.09063/) (2024)
- [Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs](https://mlsanity.com/paper/2408.04277/) (2024)
- [AdaptDel: Adaptable Deletion Rate Randomized Smoothing for Certified Robustness](https://mlsanity.com/paper/2511.09316/) (2025)

## Abstract (arXiv)

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.