LeCun co-authored LeHami: 1830s symplectic physics fixes world model collapse, 2.8x more accurate with 1/8 compute

alex_verem · x · 2026-10-19

Yann LeCun, Romina Yalovetzky and Randall Balestriero (NYU, Brown, AMI Labs) published LeHami: Symplectic Latent Dynamics for World Models (arXiv:2610.15267), fixing a core flaw in JEPA world models.

Problem: In autoregressive rollouts, each prediction feeds the next step. If the predictor slightly contracts the latent distribution each step, the shrinkage compounds until distinct states become indistinguishable.

Method: Borrowing symplectic structure from Hamiltonian mechanics — frictionless systems preserve phase-space volume — LeHami replaces the standard predictor with an action-conditioned Hamiltonian flow over a structured latent state (q, p), integrated via an exactly symplectic leapfrog step. Contraction is mathematically impossible at every step, regardless of learned parameters.

Pendulum results vs a leading JEPA baseline trained from pixels:

• 2.8x more accurate velocity prediction over the first 10 steps
• Better position tracking after 11 steps
• Constant latent volume where the baseline contracts
• Matches baseline's best accuracy with 1/8 the training compute and 32% fewer parameters
• Trained at 10fps, predicts equally well at 20/40fps; time-reversal error under 0.0001%

Caveats: A baseline using more past frames still wins goal-reaching tests, and all tests are simulated pendulums, not real-world robotics.

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