# LeHami: Symplectic Latent Dynamics for World Models

arXiv: https://arxiv.org/abs/2610.15267 · HTML: https://mlsanity.com/paper/2610.15267/

## 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 26 of its 35 references that are in the map.
- First posted on arXiv 11 Oct 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 26 of 26)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [A Closer Look at Spatiotemporal Convolutions for Action Recognition](https://mlsanity.com/paper/1711.11248/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [TinyViT: Fast Pretraining Distillation for Small Vision Transformers](https://mlsanity.com/paper/2207.10666/) (2022)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [TossingBot: Learning to Throw Arbitrary Objects with Residual Physics](https://mlsanity.com/paper/1903.11239/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Scaling Cross-Embodied Learning: One Policy for Manipulation, Navigation, Locomotion and Aviation](https://mlsanity.com/paper/2408.11812/) (2024)
- [Learning from Reward-Free Offline Data: A Case for Planning with Latent Dynamics Models](https://mlsanity.com/paper/2502.14819/) (2025)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Hierarchical Planning with Latent World Models](https://mlsanity.com/paper/2604.03208/) (2026)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning](https://mlsanity.com/paper/1703.07373/) (2017)
- [stable-worldmodel: A Platform for Reproducible World Modeling Research and Evaluation](https://mlsanity.com/paper/2605.21800/) (2026)
- [stable-pretraining-v1: Foundation Model Research Made Simple](https://mlsanity.com/paper/2511.19484/) (2025)
- [PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics](https://mlsanity.com/paper/2605.18303/) (2026)
- [HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planning](https://mlsanity.com/paper/2605.05951/) (2026)
- [Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling](https://mlsanity.com/paper/2605.00412/) (2026)

## Abstract (arXiv)

Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contract the latent distribution over long rollouts. We introduce Symplectic Hamiltonian JEPA (LeHami), which replaces the standard predictor with an action-conditioned Hamiltonian flow over a structured latent state (q, p) integrated using an exactly symplectic leapfrog step. This construction preserves phase-space volume at every rollout step and rules out uniform contraction, asymptotically stable fixed points, and merging of distinct latent states, independently of the learned parameters or action sequence. We obtain the momentum-like component from temporal derivatives of the learned position-like representation, providing an explicit second-order state for prediction and control. On conservative and actuated visual pendulum environments, LeHami substantially improves long-horizon velocity prediction over an unconstrained JEPA world model and empirically maintains constant latent volume where the baseline contracts. The learned flow also supports accurate integration at unseen sub-frame step sizes and numerical time reversal. These results show how geometric structure can provide inference-time guarantees that are complementary to representation regularization in latent world models.