# Noisy Learning for Neural ODEs Acts as a Robustness Locus Widening

arXiv: https://arxiv.org/abs/2206.08237 · HTML: https://mlsanity.com/paper/2206.08237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 28 of 28)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [MNIST-C: A Robustness Benchmark for Computer Vision](https://mlsanity.com/paper/1906.02337/) (2019)
- [Adversarial Examples Are a Natural Consequence of Test Error in Noise](https://mlsanity.com/paper/1901.10513/) (2019)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [Evaluating the Adversarial Robustness of Adaptive Test-time Defenses](https://mlsanity.com/paper/2202.13711/) (2022)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Learning continuous models for continuous physics](https://mlsanity.com/paper/2202.08494/) (2022)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradients](https://mlsanity.com/paper/2009.13145/) (2020)
- [ResNet After All? Neural ODEs and Their Numerical Solution](https://mlsanity.com/paper/2007.15386/) (2020)
- [Stateful ODE-Nets using Basis Function Expansions](https://mlsanity.com/paper/2106.10820/) (2021)
- [Improving the Robustness of Deep Neural Networks via Adversarial Training with Triplet Loss](https://mlsanity.com/paper/1905.11713/) (2019)
- [Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEs](https://mlsanity.com/paper/2201.05715/) (2022)
- [Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory](https://mlsanity.com/paper/2102.09750/) (2021)
- [Improving Neural ODEs via Knowledge Distillation](https://mlsanity.com/paper/2203.05103/) (2022)
- [Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings](https://mlsanity.com/paper/2205.11989/) (2022)

## 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.