LeHami brings Hamiltonian mechanics into JEPA with symplectic integrators to prevent latent collapse

TheTuringPost · x · 2026-11-07

• The Turing Post breaks down LeHami, by Yann LeCun, Randall Balestriero, and Romina Yalov: injecting Hamiltonian mechanics into JEPA world models to preserve phase-space volume and prevent latent collapse during long-term predictions.
• Why Hamiltonian over Lagrangian: variables are coordinates q and momenta p, yielding paired first-order update equations. The Hamiltonian H (typically kinetic + potential energy) is the central function, learned with kinetic-like K(p) and potential-like V(q, u) components, where u represents actions.
• A symplectic leapfrog integrator predicts state evolution under actions while preserving constraints. The accompanying chart contrasts the two equivalent formulations and notes LeHami rules out specific rollout-collapse modes, not prediction errors.

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