LeCun team's LeHami: symplectic Hamiltonian flow keeps JEPA world models from collapsing latent states
ylecun · x · 2026-10-30
LeCun, Balestriero and Yalovetzky propose LeHami (Symplectic Hamiltonian JEPA) on arXiv: unconstrained autoregressive predictors contract the latent distribution over long rollouts, so LeHami replaces the predictor with an action-conditioned Hamiltonian flow over a (q, p) latent state, integrated with an exactly symplectic leapfrog step.
- Phase-space volume is preserved at every rollout step, independent of learned parameters or actions, ruling out contraction and merging of latent states
- The momentum-like component is derived from temporal derivatives of the learned position representation, giving an explicit second-order state for prediction and control
- On visual pendulum environments it substantially improves long-horizon velocity prediction over unconstrained JEPA baselines, and supports integration at unseen sub-frame steps and numerical time reversal
Takeaway: geometric structure provides inference-time guarantees complementary to representation regularization in latent world models.
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