Certified Horizons: How to guarantee physics laws survive learned world models

Hongbo Wang's new paper tackles a fundamental question in representation learning for physics: when do conservation laws survive after a model learns a latent representation? The answer is a new formalism called 'certified horizons,' which precompute a worst-case bound on how many rollout steps will provably stay on a physical invariant's level set. Crucially, Wang shifts the certification target away from a learned latent Hamiltonian or scalar witness (which can conserve while drifting in true energy) and instead certifies the 'decoded physical invariant'—obtained by decoding the latent state and evaluating the known invariant. Around this object, he derives shell-horizon certificates whose budget decomposes into representation, readout, and latent-dynamics defects, with a monotone alignment bridge connecting a soft learned witness to a certified horizon for the decoded invariant.

Experiments across state, learned-lift, and pixel observations reveal that not all geometric priors survive equally. Hard canonical symplectic structure produces the longest certified horizons when phase coordinates are known, but it cannot cross a learned chart. A controlled-Lipschitz-aligned soft invariant successfully survives in the learned-representation settings tested. Pixel certification is recovered on a readout-stable sub-tube, but the Kepler problem exposes a geometric boundary where certification breaks down. The paper provides 15 pages of theory with attached code, offering a measurable, falsifiable, and actionable framework for ensuring that AI world models stay physically faithful—critical for robotics, autonomous simulation, and any deployment where physics fidelity matters.