Conformal Orbit-Valid Trust Horizons for Equivariant World Models
Learned world models are useful only over horizons on which their rollout error remains controlled. This paper studies trust-horizon certification for latent world models with known group symmetries. Using split-conformal calibration, the authors show that exact equivariance transports the calibrated trust-horizon curve over the group orbit, making rollout errors and trust horizons orbit-constant. Experiments on 2D and 3D tasks demonstrate that equivariant models achieve safe and non-vacuous orbit-valid certificates from a single calibration sector, while non-equivariant baselines incur additional costs. The certificate is a conservative distributional audit, not a global reachability guarantee.
[2606.24946] Conformal Orbit-Valid Trust Horizons for Equivariant World Models
[Submitted on 23 Jun 2026]
Title:Conformal Orbit-Valid Trust Horizons for Equivariant World Models
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Abstract:Learned world models are useful only over horizons on which their rollout error remains controlled. We study trust-horizon certification for latent world models with known group symmetries. Given a one-step latent residual and a finite-time expansion estimate, we form a raw horizon curve and calibrate it with a split-conformal multiplicative factor. On the reproducible audit set, the conformal factor is $\gamma_\alpha=1.0$: the raw certificate is already conservative under the audit protocol. Across 50 stable audits, we observe zero anti-conservative violations, corresponding to an exact-binomial 95% upper bound of 5.8% on the violation rate. Our main structural result is that exact equivariance transports a calibrated trust-horizon curve over the group orbit: when the environment dynamics, encoder, predictor, action transform, and latent metric satisfy the stated equivariance/invariance conditions, rollout errors and trust horizons are orbit-constant. Empirically, the implemented models exhibit small orbit-transport residuals, with median 1.1% and maximum 4.1% over 14 orbit audits. The certificate is also non-vacuous (median certified-to-measured horizon ratio 0.67). A certificate-level calibration-cost study shows two complementary regimes. On a symmetric 2D substrate, equivariant, plain, and augmented models are all orbit-valid from a single calibration sector -- no separation, because the substrate already makes non-equivariant baselines approximately orbit-robust. A 3D yaw audit shows the other regime: the equivariant model obtains a one-sector safe and non-vacuous orbit-valid certificate, while healthy non-equivariant baselines pay violation, slack, sharpness, or additional-sector cost. The certificate is a conservative, distributional audit rather than a global reachability guarantee, and certificate-guided subgoal spacing is not confirmed in the current 3D CEM-MPC behavior layer.
Comments: 15 pages, 6 figures
Subjects:
Machine Learning (cs.LG); Robotics (cs.RO)
Cite as: arXiv:2606.24946 [cs.LG]
(or arXiv:2606.24946v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.24946
arXiv-issued DOI via DataCite
Submission history
From: Hongbo Wang [view email] [v1] Tue, 23 Jun 2026 06:44:27 UTC (645 KB)
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