# Certified World Models: Predictability Across Configuration, Horizon, and Resolution

arXiv: https://arxiv.org/abs/2606.13092 · HTML: https://mlsanity.com/paper/2606.13092/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- First posted on arXiv 11 Jun 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Built on by (most cited first, 3 of 3)

- [Certified World Models as Sensing Clocks: Drift-Aware Deadlines for Active Perception](https://mlsanity.com/paper/2607.01537/) (2026)
- [When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models](https://mlsanity.com/paper/2606.24945/) (2026)
- [Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control](https://mlsanity.com/paper/2608.07265/) (2026)

## Abstract (arXiv)

Scale buys interpolation; structure buys certifiable transfer. A world model's average error does not say whether a particular rollout can be trusted, or for how long. For equivariant latent world models we give a predictability certificate: a computable region spanning configuration, horizon, and resolution. Under exact equivariance, rollout error is invariant over the monoid generated by k primitive symmetries and is certified from the k generators (Theorem A); universal orbit-flatness over equivariant targets characterizes equivariance at the function level (Lemma 2), so an unconstrained architecture cannot certify the property by construction. Approximate orbit-transfer defects propagate by the finite-time Lyapunov spectrum (Theorem B): expanding channels give a logarithmic horizon Tj(ε)~log(1/ε)/λj, neutral channels accumulate recurrent defect linearly, and contracting channels accumulate a bounded nonzero floor. Exact conserved charge values are certified to all horizons only at zero defect; with one-step defect η, charge-value error grows at most as Tη. Empirically, on a 40-dimensional learned model a mathbbZN-equivariant network recovers the full Lyapunov spectrum (R2=0.98-0.99) where dense and recurrent baselines fail. A cone/adapted-metric certificate reads an a-priori horizon off the model's own Jacobian, tight on uniformly hyperbolic dynamics and self-abstaining elsewhere; the resulting horizon improves a budgeted re-observation decision. For public non-equivariant world models the tangent spectrum gives a training-free candidate horizon, paired with a held-out divergence cross-check that abstains or corrects when the learned loop over-promises.