A Spectral Trajectory Objective for World Model Planning

Effective planning with world models depends not only on predictive accuracy, but also on how imagined trajectories are evaluated. Learning auxiliary planning objectives can improve control, but introduces additional training and may require task-specific supervision. We instead improve planning by redesigning the objective, without training any additional model. We introduce a spectral trajectory objective that stacks goal-relative latent residuals along an imagined rollout into a time-by-feature matrix and minimizes its horizon-normalized squared spectral norm. Unlike terminal distance, this objective considers the full predicted trajectory; unlike summed per-step errors, it accounts for alignment between residuals across time and emphasizes the dominant joint discrepancy. Across four LeWorldModel tasks and three planning horizons, Spectral improves task- and horizon-averaged success over Frobenius scoring by 13.3 percentage points, with a separate uniform-configuration evaluation yielding a similar 13.8-point gain. The same objective transfers to DINO-WM, where it shows clearer gains over terminal scoring at longer planning horizons. These results establish trajectory-objective geometry as an effective design dimension for world-model planning without additional model training.