mlsanityData to 7 Oct 2026

Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees

arXiv 2402.08090 ↗First posted 12 Feb 2024cs.LG math.OCcited by 11

Not on the map. Why?

Abstract (arXiv)

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 25 of its 50 references that are in the map. First posted on arXiv 12 Feb 2024.

Builds on

25 of 50 references.

References · 25

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13 more
  1. 2020Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systemscited by 32
  2. 2018Learning Contracting Vector Fields For Stable Imitation Learningcited by 20
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 7; 2026: 2.

11 papers.

  1. 2025Predictability Enables Parallelization of Nonlinear State Space Modelscited by 7
  2. 2025R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networkscited by 2
  3. 2025Geometric Contact Flows: Contactomorphisms for Dynamics and Controlcited by 2
  4. 2025Characterizing control between interacting subsystems with deep Jacobian estimationcited by 2
  5. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  6. 2025Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representationscited by 1
  7. 2024Tracking control of latent dynamic systems with application to spacecraft attitude controlcited by 0
  8. 2025Stable neural networks and connections to continuous dynamical systemscited by 0
  9. 2025Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioningcited by 0
  10. 2026Stability Enhanced Gaussian Process Variational Autoencoderscited by 0
  11. 2026Manifold-Stable Flow Matchingcited by 0