Certified geometric robustness -- Super-DeepG

2026-04-27

AI Summary

This work addresses the challenge of verifying the robustness of neural networks under geometric perturbations—including rotation, scaling, shearing, and translation—by proposing Super-DeepG, a novel verification method that integrates an improved linear relaxation scheme with optimized Lipschitz constant estimation. For the first time, it incorporates a GPU-accelerated formal verification framework, achieving both high certification accuracy and significantly enhanced computational efficiency. Experimental results demonstrate that Super-DeepG outperforms existing approaches in both performance and precision on geometric robustness certification tasks. To foster further research in this direction, the authors publicly release an efficient implementation of their method.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Safety-critical applications are required to perform as expected in normal operations. Image processing functions are often required to be insensitive to small geometric perturbations such as rotation, scaling, shearing or translation. This paper addresses the formal verification of neural networks against geometric perturbations on their image dataset. Our method Super-DeepG improves the reasoning used in linear relaxation techniques and Lipschitz optimization, and provides an implementation that leverages GPU hardware. By doing so, Super-DeepG achieves both precision and computational efficiency of robustness certification, to an extent that outperforms prior work. Super-DeepG is shared as an open-source tool on GitHub.

Problem

• geometric robustness
• formal verification
• neural networks
• geometric perturbations
• safety-critical applications

Innovation

• geometric robustness
• formal verification
• linear relaxation
• Lipschitz optimization
• GPU acceleration