When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models

Short summary

Researchers propose certified-horizon methods to verify when conservation laws remain valid in learned latent representations of physical world models. The innovation is certifying decoded physical invariants rather than latent Hamiltonians, with bounds decomposed into representation, readout, and dynamics defects. Tests show hard symplectic structure yields longest horizons but soft Lipschitz-aligned invariants survive better in learned-representation settings.

• •Novel certification method for conservation laws in learned latent representations of physics
• •Certifies decoded physical invariants rather than latent Hamiltonians to track true energy
• •Hard symplectic structure and soft invariants show different transfer properties across representations

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