LeHami: Symplectic Latent Dynamics for World Models

Key points

• Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contract the latent distribution over long rollouts.1
• 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.1
• 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.1
• These results show how geometric structure can provide inference-time guarantees that are complementary to representation regularization in latent world models.1

Sources (1)

• [1]LeHami: Symplectic Latent Dynamics for World Models
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 11, 01:28 AM

  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.

  Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contract the latent distribution over long rollouts.

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