mlsanityData to 7 Oct 2026

STEER: Simple Temporal Regularization For Neural ODEs

arXiv 2006.10711 ↗First posted 18 Jun 2020cs.LG stat.MLcited by 58

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Abstract (arXiv)

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have shown that regularizing the dynamics of the ODE can partially alleviate this. In this paper we propose a new regularization technique: randomly sampling the end time of the ODE during training. The proposed regularization is simple to implement, has negligible overhead and is effective across a wide variety of tasks. Further, the technique is orthogonal to several other methods proposed to regularize the dynamics of ODEs and as such can be used in conjunction with them. We show through experiments on normalizing flows, time series models and image recognition that the proposed regularization can significantly decrease training time and even improve performance over baseline models.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2020.

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Citing papers per year: 2021: 12; 2022: 12; 2023: 10; 2024: 12; 2025: 8; 2026: 4.

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  1. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 99
  2. 2021Stiff Neural Ordinary Differential Equationscited by 77
  3. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  4. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  5. 2021Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristicscited by 26
  6. 2022Neural Laplace: Learning diverse classes of differential equations in the Laplace domaincited by 24
  7. 2022Neural Integral Equationscited by 23
  8. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  9. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  10. 2022Homotopy-based training of NeuralODEs for accurate dynamics discoverycited by 14
  11. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  12. 2024When are dynamical systems learned from time series data statistically accurate?cited by 14
38 more
  1. 2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
  2. 2021Second-Order Neural ODE Optimizercited by 11
  3. 2023Neural Markov Jump Processescited by 11
  4. 2024Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methodscited by 11
  5. 2021How Does Momentum Benefit Deep Neural Networks Architecture Design? A Few Case Studiescited by 10
  6. 2022torchode: A Parallel ODE Solver for PyTorchcited by 10
  7. 2022Sparsity in Continuous-Depth Neural Networkscited by 10
  8. 2022TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speedcited by 8
  9. 2024Simulation-Free Training of Neural ODEs on Paired Datacited by 8
  10. 2024Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation lawcited by 7
  11. 2025Bidirectional Normalizing Flow: From Data to Noise and Backcited by 7
  12. 2021Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flowscited by 6
  13. 2022Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEscited by 6
  14. 2024Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODEcited by 6
  15. 2022Continuous Deep Equilibrium Models: Training Neural ODEs faster by integrating them to Infinitycited by 5
  16. 2024LaTiM: Longitudinal representation learning in continuous-time models to predict disease progressioncited by 5
  17. 2024Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methodscited by 5
  18. 2021Multi-Resolution Continuous Normalizing Flowscited by 4
  19. 2023Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!cited by 4
  20. 2022A memory-efficient neural ODE framework based on high-level adjoint differentiationcited by 3
  21. 2023Faster Training of Neural ODEs Using Gauss-Legendre Quadraturecited by 3
  22. 2023LMT: Longitudinal Mixing Training, a Framework to Predict Disease Progression from a Single Imagecited by 3
  23. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  24. 2025SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimationcited by 3
  25. 2025The Vanishing Gradient Problem for Stiff Neural Differential Equationscited by 3
  26. 2026Continuous-Time Piecewise-Linear Recurrent Neural Networkscited by 3
  27. 2023Trainability, Expressivity and Interpretability in Gated Neural ODEscited by 2
  28. 2024Graph Neural Aggregation-diffusion with Metastabilitycited by 2
  29. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  30. 2021Meta-Solver for Neural Ordinary Differential Equationscited by 1
  31. 2021Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamicscited by 1
  32. 2021STR-GODEs: Spatial-Temporal-Ridership Graph ODEs for Metro Ridership Predictioncited by 1
  33. 2021Latent Time Neural Ordinary Differential Equationscited by 1
  34. 2022Semi-Equivariant Continuous Normalizing Flows for Target-Aware Molecule Generationcited by 1
  35. 2023On Tuning Neural ODE for Stability, Consistency and Faster Convergencecited by 1
  36. 2024Divide And Conquer: Learning Chaotic Dynamical Systems With Multistep Penalty Neural Ordinary Differential Equationscited by 1
  37. 2024Discover physical concepts and equations with machine learningcited by 1
  38. 2025Continuum Dropout for Neural Differential Equationscited by 1

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