Efficient Certified Training and Robustness Verification of Neural ODEs
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Date
2023-02-01
Publication Type
Conference Paper
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yes
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Abstract
Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial perturbations, they were recently shown to be vulnerable to strong adversarial attacks, highlighting the need for formal guarantees. However, despite significant progress in robustness verification for standard feed-forward architectures, the verification of high dimensional NODEs remains an open problem. In this work, we address this challenge and propose GAINS, an analysis framework for NODEs combining three key ideas: (i) a novel class of ODE solvers, based on variable but discrete time steps, (ii) an efficient graph representation of solver trajectories, and (iii) a novel abstraction algorithm operating on this graph representation. Together, these advances enable the efficient analysis and certified training of high-dimensional NODEs, by reducing the runtime from an intractable $O(\exp(d)+\exp(T))$ to $O(d+T^2 \log^2T)$ in the dimensionality $d$ and integration time $T$. In an extensive evaluation on computer vision (MNISTand Fashion-MNIST) and time-series forecasting (Physio-Net) problems, we demonstrate the effectiveness of both our certified training and verification methods.
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published
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Book title
The Eleventh International Conference on Learning Representations (ICLR 2023)
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Publisher
OpenReview
Event
11th International Conference on Learning Representations (ICLR 2023)
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Subject
Neural ODEs; Adversarial Robustness; Certified Robustness; Robustness Verification; Certified Training
Organisational unit
03948 - Vechev, Martin / Vechev, Martin
Notes
Funding
101070617/22.00164 - European Lighthouse on Secure and Safe AI (SBFI)
MB22.00088 - SafeAI: Certified Safe, Fair and Robust Artificial Intelligence (SBFI)
MB22.00088 - SafeAI: Certified Safe, Fair and Robust Artificial Intelligence (SBFI)