Symplectic Latent Dynamics for World Models

A paper submitted to arXiv on 11 October 2026 by Romina Yalovetzky introduces Symplectic Hamiltonian JEPA (LeHami), a world model that replaces the standard joint-embedding predictive architecture predictor with an action-conditioned Hamiltonian flow over a structured latent state (q, p) integrated by an exactly symplectic leapfrog step. The construction preserves phase-space volume at every rollout step and rules out uniform contraction, asymptotically stable fixed points and merging of distinct latent states regardless of learned parameters or action sequence. On conservative and actuated visual pendulum environments, LeHami substantially improves long-horizon velocity prediction over an unconstrained JEPA world model and maintains constant latent volume where the baseline contracts, while also supporting accurate integration at unseen sub-frame step sizes and numerical time reversal.

Computer Science Machine Learning Submitted on 11 Oct 2026 Title:LeHami: Symplectic Latent Dynamics for World Models View PDF https://arxiv.org/pdf/2610.15267 HTML experimental https://arxiv.org/html/2610.15267v1 Abstract: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. Submission history From: Romina Yalovetzky view email https://arxiv.org/show-email/47f36e5e/2610.15267 v1 Sun, 11 Oct 2026 01:28:41 UTC 3,897 KB Additional Features Current browse context: cs.LG References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .