A Control Theory of Predictability in Latent World Models

2026-07-11

AI Summary

This work addresses a critical limitation in existing latent-variable world models, which rely on average prediction error over training data for training and selection—a metric that fails to reflect actual controller performance due to a mismatch between the evaluation distribution and the distribution queried by the planner. The authors propose instead to center model assessment on the discrepancy between predicted and true costs over states reachable by the planner. They establish, for the first time, a rigorous theoretical link between this discrepancy and control suboptimality, proving it provides a valid upper bound on performance loss, whereas conventional prediction errors neither bound nor track performance. Leveraging control theory, spectral analysis, and non-normal operator theory, they decompose the discrepancy into an intrinsic manifold residual and an off-manifold divergence term, and introduce a fidelity score to quantify alignment of the planner’s reachable distribution. Experiments on synthetic systems and model predictive control confirm that the proposed metric reliably tracks control performance, while single-step prediction error shows virtually no correlation.

Abstract

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.

Problem

• latent world models
• predictive error
• model-based control
• off-manifold divergence
• plan-cost discrepancy

Innovation

• latent world models
• predictive control
• off-manifold generalization
• plan-cost discrepancy
• model-based planning