Certified World Models as Sensing Clocks: Drift-Aware Deadlines for Active Perception

Learned world models typically assume that observations arrive synchronously, an abstraction inherited from simulators that return a complete state vector at each environment step. Physical sensing instead operates at heterogeneous rates, leaving most observation channels stale at any given instant. Interpolating stale channels introduces measurements that were never observed, while downsampling to the slowest sensor discards valid measurements. A natural alternative is to zero-order-hold the most recent reading and provide the known sampling schedule to the model through two features, staleness and time-to-refresh. We test this prediction using transformer world models across three regimes of increasing causal coupling: open-loop rollouts in continuous-control locomotion, closed-loop model-predictive planning in which each learned model serves as the planner dynamics, and a linear latched-actuator system in which refresh events apply a zero-order-held command to the plant. Our findings show that the effectiveness of time-to-refresh depends on the causal role of the sampling schedule, specifically when refresh events affect the system rather than merely report its state. These results establish when sampling schedules provide useful information for predictive world models operating under asynchronous physical observations.

In world model planning, sensing inputs pass through an encoder and predictor before affecting planner decisions, so final task success alone cannot reveal where sensing disturbances attenuate or persist in the pipeline. We apply 10 visual and temporal sensing degradations to a world model planner and track their effects across representation, future prediction, planner preference, and physical outcome using paired evaluation on the same 50 tasks. The relative impact of degradations was not preserved across stages: large representation shifts could attenuate downstream, while smaller initial shifts could persist to the outcome, and internal-response ordering did not directly match physical-outcome ordering. Temporal degradations also showed distinct patterns: even with similar overall changes in observation history, responses differed substantially with the location of corrupted information and the planner's actual exposure. This non-uniform stage-wise response was also observed in secondary evaluations with another manipulation task and a different world model. Stage-wise diagnosis can therefore identify where sensing disturbances attenuate or persist and help prioritize subsequent model verification and sensing mitigation.

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 $T_j(ε)\sim\log(1/ε)/λ_j$, 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 $\mathbb{Z}_N$-equivariant network recovers the full Lyapunov spectrum ($R^2=0.98$-$0.99$) 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.