Reproduce “LeHami: Symplectic Latent Dynamics for World Models” on OpenResearch

About this paper

Romina Yalovetzky, Randall Balestriero, Yann LeCun

LeHami models dynamics by encoding position-like and momentum-like latents, then advancing them with an action-conditioned Hamiltonian step that preserves latent volume. On a conservative pendulum, its probe reports 2.8 times lower angular-velocity error over the first ten rollout steps and 1.3 times lower at the horizon’s end. This guarantee does not bound prediction error; untied-window LeWorldModel scores higher on velocity-goal planning.

Key insights

• Symplecticity rules out uniform latent contraction, stable attracting fixed points, and the merging of distinct states across a rollout, but does not guarantee accurate predictions or prevent stretching and shearing.
• The derivative-based latent momentum provides direction-sensitive motion information; on the actuated pendulum, a 25-neighbour probe achieved velocity R² of 0.889, while LeWM’s reported velocity probes were below the predict-the-mean floor.
• The structural prior brings trade-offs: preserving phase-space volume may not suit strongly dissipative dynamics, and improved velocity representation does not translate into better performance on every planning objective.

Summary by alphaXiv.