mlsanityData to 14 Oct 2026

Ortho-ODE: Enhancing Robustness and of Neural ODEs against Adversarial Attacks

arXiv 2305.09179 ↗First posted 16 May 2023cs.LG cs.AI cs.CRcited by 0

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Abstract (arXiv)

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth. NODEs were designed to tackle the irregular time series problem. However, NODEs have demonstrated robustness against various noises and adversarial attacks. This paper is about the natural robustness of NODEs and examines the cause behind such surprising behaviour. We show that by controlling the Lipschitz constant of the ODE dynamics the robustness can be significantly improved. We derive our approach from Grownwall's inequality. Further, we draw parallels between contractivity theory and Grownwall's inequality. Experimentally we corroborate the enhanced robustness on numerous datasets - MNIST, CIFAR-10, and CIFAR 100. We also present the impact of adaptive and non-adaptive solvers on the robustness of NODEs.

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References · 22

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2016Adversarial Machine Learning at Scalecited by 936
  5. 2017Adversarial Examples for Evaluating Reading Comprehension Systemscited by 571
  6. 2019Augmented Neural ODEscited by 397
  7. 2017Adversarial Attacks on Neural Network Policiescited by 320
  8. 2019Adversarial Attacks and Defenses in Images, Graphs and Text: A Reviewcited by 237
  9. 2019You Only Propagate Once: Accelerating Adversarial Training via Maximal Principlecited by 183
  10. 2020Dissecting Neural ODEscited by 153
  11. 2018LaVAN: Localized and Visible Adversarial Noisecited by 113
  12. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
10 more
  1. 2020Training robust neural networks using Lipschitz boundscited by 99
  2. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  3. 2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 65
  4. 2020A Panda? No, It's a Sloth: Slowdown Attacks on Adaptive Multi-Exit Neural Network Inferencecited by 61
  5. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 38
  6. 2021The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initializationcited by 33
  7. 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
  8. 2021Robust Implicit Networks via Non-Euclidean Contractionscited by 20
  9. 2019Robust Design of Deep Neural Networks against Adversarial Attacks based on Lyapunov Theorycited by 13
  10. 2021Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memorycited by 11

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