Operator-on-F complements value-equivalence: a planning-time diagnostic for latent world models

Planning-time intervention fidelity is a distinct, measurable property of a learned world model: whether the model's own open-loop transitions move task variables the way matched environment interventions do. In the settings we test, it is neither revealed by reward fit nor ensured by task-anchored training. Across released TD-MPC2 checkpoint sizes, episode return falls as an operator-error diagnostic on task observables grows, while reward-prediction error stays small and nearly flat, and a self-supervised world model trained without task signal preserves the same operator substantially better than a task-anchored model on the shared task. A capture-gated matched-intervention audit then localizes what fails. On Cheetah, three LeWorldModel checkpoints capture the current task query and support decodable real intervention effects; however, their imagined five-step effects are worse than predicting no effect and worse than an environment-endpoint oracle. The failure is task-direction rotation with excess gain, not feature collapse. This severe pattern is conditional: five PreJEPA seeds retain an oracle-relative deficit without it, Finger Spin experiments extend the deficit beyond locomotion with heterogeneous severity across seeds, and shared-bank effect geometry is both candidate- and support-dependent. We also test practice-side questions. In DreamerV3 the posterior distribution, not its sample, carries the current query; ensemble disagreement ranks error only near training support; and a frozen support-aware score degrades held-out error ranking in both tested transfer directions while native disagreement remains informative in both. We conclude that intervention fidelity must be audited directly, capture-first, on the model's native interface.

We study how to predict the downstream closed-loop performance of a learned latent world model from validation-time diagnostics alone. Choosing the right checkpoint from a world-model training run is difficult: validation loss and multi-step prediction RMSE keep improving long after closed-loop performance has collapsed. We present a suite of structural validation-time diagnostics drawn from optimal-control theory and apply them to Gymnasium's LunarLander v3, which features shaped rewards. We train an RSSM [5, 4] world model on it and treat per checkpoint CEM-MPC return as the oracle for closed-loop quality. By evaluating 40 metrics against this oracle, we find that the strongest single predictor is the Reward Observability Fraction (ROF), which measures the reward predictor's dependence on the observable subspace. We combine ROF with three structural regularizers into a single-number offline checkpoint selection score, the Composite Reward Observability Fraction (CROF). The CROF-selected world model trains a model-based A2C policy that beats a fairly evaluated model-free A2C baseline by ~24.5 return points while using ~65x fewer real-environment interactions, and the same world model also drives a strong zero-shot CEM-MPC policy. Code and data: https://github.com/nsmoly/LunarLander_RSSM.

Latent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single- or multi-step rollout loss on held-out data, as the training and model-selection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner's suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.