Three-in-One World Model: Energy-Based Consistency, Prediction, and Counterfactual Inference for Marketing Intervention

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.

Driving world models are often interpreted as counterfactual simulators for observed driving episodes: given a factual driving log, they are asked what would have happened under an alternative ego action. In this paper, we identify a fundamental mismatch between this goal and direct action-conditioned prediction. The direct prediction uses the shared history and the alternative action but not the factual continuation observed after that history. It can therefore generate a plausible future without preserving what actually happened in this episode. We formalize this gap using the causal recipe of abduction, action, and prediction and study it in a setting with a short time horizon, where the alternative ego action does not alter how surrounding agents evolve. To make the gap measurable, we construct a controlled simulation benchmark with factual outcomes and matched counterfactual outcomes. Across two representative world models, direct predictions fail to match the counterfactual ground truth, supporting our analysis. As a constructive check of this analysis, we introduce a deliberately simple, training-free pipeline that moves observed evidence into the counterfactual view and lets the frozen model complete what remains unknown. Even this simple construction raises the overall recovered fraction substantially and reduces perceptual distance to the matched counterfactual on both models. We hope this work draws attention to this gap and motivates better counterfactual prediction methods for driving world models.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.