FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs
Machine Learning
2023-12-25 v4
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.
Cite
@article{arxiv.2210.16940,
title = {FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs},
author = {Yujia Huang and Ivan Dario Jimenez Rodriguez and Huan Zhang and Yuanyuan Shi and Yisong Yue},
journal= {arXiv preprint arXiv:2210.16940},
year = {2023}
}