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.

翻译：安全关键型应用需在正常操作中按预期执行。图像处理功能通常需对旋转、缩放、剪切或平移等微小几何扰动不敏感。本文针对神经网络在图像数据集上抵御几何扰动的形式化验证问题开展研究。我们的方法Super-DeepG改进了线性松弛技术与Lipschitz优化中的推理机制，并提供了利用GPU硬件的实现方案。由此，Super-DeepG在鲁棒性认证的精度与计算效率方面均达到超越先前工作的水平。Super-DeepG已作为开源工具在GitHub上发布。