mlsanityData to 14 Oct 2026

Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Models

arXiv 2609.19674 ↗First posted 17 Sep 2026cs.LGcited by 0

On the map: World models → Latent predictive world models

Abstract (arXiv)

A learned simulator can reproduce its training conditions accurately yet fail in two distinct ways once those conditions change. Over long rollouts, small errors accumulate until the trajectory drifts away from physically plausible behavior; under an intervention on a physical parameter, the model may continue to follow the law seen during training rather than the intervened one. We show that these two failures require different structural remedies. Evolving a learned energy with a symplectic integrator preserves the geometry of the conservative dynamics and keeps rollouts bounded and physically meaningful for up to 100× the training horizon, while equal-capacity predictors, an energy-regularized predictor, and a tuned neural ODE diverge. By contrast, encoding the physical coupling through an explicit linear factorization enables the model to follow a never-seen sign of that coupling, whereas an unrestricted parameterization remains locked to the training law. Crucially, the two mechanisms are separable: removing the structure responsible for long-horizon stability leaves counterfactual transfer intact, while removing the factorized coupling destroys counterfactual transfer without eliminating stability. This double dissociation, established with matched controls that remove or replace one structural component at a time, persists beyond the headline three-body system and remains visible when the physical state must be inferred from pixels rather than provided directly. The result is a concrete design principle for physical world models: long-horizon stability and changed-law generalization arise from distinct structural commitments, and each can be imposed deliberately without requiring the other.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Latent predictive world models, one of 11 directions in World models. Builds on 31 of its 40 references that are in the map. First posted on arXiv 17 Sep 2026.

Builds on

31 of 40 references.

Closest ancestors · 2

Same direction, newest first

  1. 2026PhyGround: Benchmarking Physical Reasoning in Generative World Models11 May
  2. 2026Causal-JEPA: Learning World Models through Object-Level Latent Masking11 Feb

Other references · 29

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  5. 2025V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planningcited by 809
  6. 2019Hamiltonian Neural Networkscited by 712
  7. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  8. 2019CLEVRER: CoLlision Events for Video REpresentation and Reasoningcited by 484
  9. 2020Lagrangian Neural Networkscited by 398
  10. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  11. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  12. 2021Physion: Evaluating Physical Prediction from Vision in Humans and Machinescited by 153
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  2. 2019Hamiltonian Generative Networkscited by 137
  3. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
  4. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 79
  5. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 67
  6. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  7. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 47
  8. 2020Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Datacited by 40
  9. 2021LEADS: Learning Dynamical Systems that Generalize Across Environmentscited by 40
  10. 2020Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Controlcited by 38
  11. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  12. 2025"PhyWorldBench": A Comprehensive Evaluation of Physical Realism in Text-to-Video Modelscited by 36
  13. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 34
  14. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  15. 2021Adaptable Hamiltonian neural networkscited by 21
  16. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 18
  17. 2021Learning Contact Dynamics using Physically Structured Neural Networkscited by 10

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