mlsanityData to 7 Oct 2026

LyaNet: A Lyapunov Framework for Training Neural ODEs

arXiv 2202.02526 ↗First posted 5 Feb 2022cs.LG cs.AIcited by 43

Not on the map. Why?

Abstract (arXiv)

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 34 of its 44 references that are in the map. First posted on arXiv 5 Feb 2022.

Builds on

34 of 44 references.

References · 34

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  5. 2019Deep Equilibrium Modelscited by 603
  6. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  7. 2019Augmented Neural ODEscited by 396
  8. 2017Stable Architectures for Deep Neural Networkscited by 340
  9. 2018Certified Defenses against Adversarial Examplescited by 305
  10. 2018A Lyapunov-based Approach to Safe Reinforcement Learningcited by 278
  11. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  12. 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 229
22 more
  1. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  2. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  3. 2018Differentiable MPC for End-to-end Planning and Controlcited by 178
  4. 2020Torchattacks: A PyTorch Repository for Adversarial Attackscited by 156
  5. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  6. 2020Dissecting Neural ODEscited by 150
  7. 2020Neural Lyapunov Controlcited by 142
  8. 2020Learning Stable Deep Dynamics Modelscited by 110
  9. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 87
  10. 2021Stabilizing Equilibrium Models by Jacobian Regularizationcited by 71
  11. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  12. 2020Continuous-in-Depth Neural Networkscited by 40
  13. 2021Adversarial Robustness with Semi-Infinite Constrained Learningcited by 39
  14. 2016Learning Model Predictive Control for iterative tasks. A Data-Driven Control Frameworkcited by 38
  15. 2020"Hey, that's not an ODE": Faster ODE Adjoints via Seminormscited by 35
  16. 2019Control Regularization for Reduced Variance Reinforcement Learningcited by 34
  17. 2021Physics-Informed Neural Nets for Control of Dynamical Systemscited by 31
  18. 2016A Lyapunov Analysis of Momentum Methods in Optimizationcited by 28
  19. 2020Learning Lyapunov Functions for Hybrid Systemscited by 24
  20. 2021Learning by Turning: Neural Architecture Aware Optimisationcited by 23
  21. 2021Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systemscited by 17
  22. 2019A Control Lyapunov Perspective on Episodic Learning via Projection to State Stabilitycited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 6; 2024: 9; 2025: 10; 2026: 9.

43 papers.

Sort:

By area:

  1. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  2. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  3. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  4. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  5. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  6. 2023Lyapunov-Stable Deep Equilibrium Modelscited by 10
  7. 2022Learning Robust State Observers using Neural ODEs (longer version)cited by 6
  8. 2024Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddingscited by 6
  9. 2022Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learningcited by 5
  10. 2022Robust Prototypical Few-Shot Organ Segmentation with Regularized Neural-ODEscited by 5
  11. 2024DeNOTS: Stable Deep Neural ODEs for Time Seriescited by 5
  12. 2022FI-ODE: Certifiably Robust Forward Invariance in Neural ODEscited by 3
31 more
  1. 2023Efficient Certified Training and Robustness Verification of Neural ODEscited by 3
  2. 2024Certified Robust Invariant Polytope Training in Neural Controlled ODEscited by 3
  3. 2025Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvementscited by 3
  4. 2026Lyapunov Probes for Hallucination Detection in Large Foundation Modelscited by 3
  5. 2022Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objectscited by 2
  6. 2023CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Predictioncited by 2
  7. 2024Stable Autonomous Flow Matchingcited by 2
  8. 2024Physics-constrained coupled neural differential equations for one dimensional blood flow modelingcited by 2
  9. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  10. 2025LyTimeT: Towards Robust and Interpretable State-Variable Discoverycited by 2
  11. 2024ICODE: Modeling Dynamical Systems with Extrinsic Input Informationcited by 1
  12. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  13. 2025Random Spiking Neural Networks are Stable and Spectrally Simplecited by 1
  14. 2026Discovering Data Manifold Geometry through Geometric Propertiescited by 1
  15. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  16. 2022Noisy Learning for Neural ODEs Acts as a Robustness Locus Wideningcited by 0
  17. 2022Improved Batching Strategy For Irregular Time-Series ODEcited by 0
  18. 2023PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEscited by 0
  19. 2024Lyapunov Neural ODE State-Feedback Control Policiescited by 0
  20. 2024Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learningcited by 0
  21. 2025DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecastingcited by 0
  22. 2025TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flowscited by 0
  23. 2025Robust Convolution Neural ODEs via Contractivity-promoting regularizationcited by 0
  24. 2025Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustnesscited by 0
  25. 2025Control of dynamical systems with neural networkscited by 0
  26. 2026Bridging Discrete Marks and Continuous Dynamics: Dual-Path Cross-Interaction for Marked Temporal Point Processescited by 0
  27. 2026Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systemscited by 0
  28. 2026Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systemscited by 0
  29. 2026Lyapunov-Guided Training for Hardware-Safe Neural Networks Under Fixed-Point Arithmeticcited by 0
  30. 2026Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategiescited by 0
  31. 2026Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guaranteescited by 0