FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs

TL;DR

This paper introduces FI-ODE, a framework for training Neural ODEs with provable safety guarantees, applicable to control and image classification, ensuring robustness and forward invariance.

Contribution

It presents the first method to train Neural ODE policies with certifiable safety guarantees and extends the framework to adversarial robustness in image classification.

Findings

Achieved non-vacuous certified safety guarantees in Neural ODE control policies.

Extended the framework to certify adversarial robustness in image classifiers.

Demonstrated effectiveness through experiments in control and image classification tasks.

Abstract

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.