Conformal trust horizons certify safe rollouts for equivariant world models

Learned world models are only useful as long as their rollout error stays bounded. Hongbo Wang's new paper tackles trust-horizon certification by exploiting group symmetries in the latent dynamics. The core idea is to form a raw horizon curve from a one-step latent residual and a finite-time expansion estimate, then calibrate it using a split-conformal multiplicative factor. On the reproducible audit set, the conformal factor is exactly 1.0, meaning the raw certificate is already conservative. Across 50 stable audits, zero anti-conservative violations were observed, corresponding to an exact-binomial 95% upper bound of 5.8% on the violation rate.

The main structural result shows that exact equivariance transports the calibrated trust-horizon curve over the group orbit, making rollout errors and trust horizons orbit-constant under the right conditions. Empirically, the models exhibit small orbit-transport residuals — median 1.1%, maximum 4.1% over 14 orbit audits. The certificate is also non-vacuous, with a median certified-to-measured horizon ratio of 0.67. Two complementary regimes are identified: on a symmetric 2D substrate, equivariant, plain, and augmented models all produce orbit-valid certificates from a single calibration sector; on a 3D yaw audit, only the equivariant model obtains a one-sector safe and non-vacuous certificate, while non-equivariant baselines incur penalties in violation, slack, or additional calibration cost. The certificate is a conservative distributional audit, not a global reachability guarantee.