Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework in two settings: certified adversarial robustness for image classification, and certified safety in continuous control. Notably, our method empirically produces superior adversarial robustness guarantees compared to prior work on certifiably robust Neural ODEs (including implicit-depth models).

翻译：前向不变性是控制理论中长期研究的一种性质，用于证明动力系统在所有时间内始终保持在某个预设状态集合内，并具有鲁棒性保证（例如，该性质在扰动下依然成立）。我们提出一个通用框架，用于训练并可证明地认证神经常微分方程中的鲁棒前向不变性。我们将该框架应用于两种场景：图像分类的可认证对抗鲁棒性，以及连续控制中的可认证安全性。值得注意的是，我们的方法在可认证鲁棒神经常微分方程（包括隐式深度模型）中，相较于先前工作，经验上生成了更优的对抗鲁棒性保证。