mlsanityData to 14 Oct 2026

Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations

arXiv 2304.02976 ↗First posted 6 Apr 2023eess.SY cs.LG cs.SYcited by 8

Not on the map. Why?

Abstract (arXiv)

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 16 of its 35 references that are in the map. First posted on arXiv 6 Apr 2023.

Builds on

16 of 35 references.

References · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2016An overview of gradient descent optimization algorithmscited by 1,033
  5. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  6. 2019Augmented Neural ODEscited by 397
  7. 2017Stable Architectures for Deep Neural Networkscited by 341
  8. 2020Training robust neural networks using Lipschitz boundscited by 99
  9. 2018Seq2Sick: Evaluating the Robustness of Sequence-to-Sequence Models with Adversarial Examplescited by 94
  10. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  11. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 45
  12. 2020Stable Neural Flowscited by 25
4 more
  1. 2021Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Designcited by 18
  2. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  3. 2021Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guaranteescited by 10
  4. 2017Contracting Nonlinear Observers: Convex Optimization and Learning from Datacited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 1; 2026: 1.

8 papers.

  1. 2024Learning to Boost the Performance of Stable Nonlinear Systemscited by 7
  2. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  3. 2024Learning Stable and Passive Neural Differential Equationscited by 2
  4. 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approachcited by 2
  5. 2023RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustnesscited by 1
  6. 2024On Dissipativity of Cross-Entropy Loss in Training ResNetscited by 1
  7. 2025Circuit realization and hardware linearization of monotone operator equilibrium networkscited by 1
  8. 2026LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layerscited by 0