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Noisy Learning for Neural ODEs Acts as a Robustness Locus Widening

arXiv 2206.08237 ↗First posted 16 Jun 2022cs.LGcited by 0

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Abstract (arXiv)

We investigate the problems and challenges of evaluating the robustness of Differential Equation-based (DE) networks against synthetic distribution shifts. We propose a novel and simple accuracy metric which can be used to evaluate intrinsic robustness and to validate dataset corruption simulators. We also propose methodology recommendations, destined for evaluating the many faces of neural DEs' robustness and for comparing them with their discrete counterparts rigorously. We then use this criteria to evaluate a cheap data augmentation technique as a reliable way for demonstrating the natural robustness of neural ODEs against simulated image corruptions across multiple datasets.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 28 of its 34 references that are in the map. First posted on arXiv 16 Jun 2022.

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References · 28

  1. 2018Neural Ordinary Differential Equationscited by 3,733
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  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  4. 2020The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalizationcited by 1,842
  5. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,366
  6. 2020Measuring Robustness to Natural Distribution Shifts in Image Classificationcited by 452
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  12. 2019MNIST-C: A Robustness Benchmark for Computer Visioncited by 137
16 more
  1. 2019Adversarial Examples Are a Natural Consequence of Test Error in Noisecited by 114
  2. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  3. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  4. 2022Evaluating the Adversarial Robustness of Adaptive Test-time Defensescited by 64
  5. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  6. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  7. 2022Learning continuous models for continuous physicscited by 28
  8. 2021Framing RNN as a kernel method: A neural ODE approachcited by 23
  9. 2020Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradientscited by 22
  10. 2020ResNet After All? Neural ODEs and Their Numerical Solutioncited by 20
  11. 2021Stateful ODE-Nets using Basis Function Expansionscited by 14
  12. 2019Improving the Robustness of Deep Neural Networks via Adversarial Training with Triplet Losscited by 13
  13. 2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
  14. 2021Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memorycited by 11
  15. 2022Improving Neural ODEs via Knowledge Distillationcited by 1
  16. 2022Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddingscited by 1

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