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FI-ODE: Certified and Robust Forward Invariance in Neural ODEs

Huang, Yujia and Jimenez Rodriguez, Ivan Dario and Zhang, Huan and Shi, Yuanyuan and Yue, Yisong (2022) FI-ODE: Certified and Robust Forward Invariance in Neural ODEs. . (Unpublished)

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We study how to certifiably enforce forward invariance properties in neural ODEs. Forward invariance implies that the hidden states of the ODE will stay in a "good" region, and a robust version would hold even under adversarial perturbations to the input. Such properties can be used to certify desirable behaviors such as adversarial robustness (the hidden states stay in the region that generates accurate classification even under input perturbations) and safety in continuous control (the system never leaves some safe set). We develop a general approach using tools from non-linear control theory and sampling-based verification. Our approach empirically produces the strongest adversarial robustness guarantees compared to prior work on certifiably robust ODE-based models (including implicit-depth models).

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Huang, Yujia0000-0001-7667-8342
Jimenez Rodriguez, Ivan Dario0000-0001-9065-5227
Zhang, Huan0000-0002-1096-4255
Shi, Yuanyuan0000-0002-6182-7664
Yue, Yisong0000-0001-9127-1989
Additional Information:This work is funded in part by AeroVironment and NSF #1918865.
Funding AgencyGrant Number
Record Number:CaltechAUTHORS:20221219-234122405
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118474
Deposited By: George Porter
Deposited On:21 Dec 2022 00:58
Last Modified:21 Dec 2022 00:58

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