Certified geometric robustness -- Super-DeepG

TL;DR

Super-DeepG is a GPU-accelerated method for formally verifying neural network robustness against small geometric image perturbations, outperforming prior approaches in precision and efficiency.

Contribution

It introduces an improved reasoning framework combining linear relaxation and Lipschitz optimization, with an open-source implementation leveraging GPU hardware.

Findings

Outperforms prior work in robustness certification accuracy

Achieves high computational efficiency through GPU acceleration

Provides a practical open-source tool for geometric robustness verification

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.