FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs
This work addresses safety and robustness issues in neural dynamical systems, particularly for control and classification tasks, but it is incremental as it builds on existing control theory concepts.
The authors tackled the problem of ensuring that Neural ODEs remain within safe states under perturbations by proposing a framework for training and certifying robust forward invariance, achieving non-vacuous certified guarantees for continuous control and adversarial robustness in image classification.
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 to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.