Regularizing Geometry and Error Propagation in Latent World Models

A latent world model can have a well-regularized representation distribution yet make unreliable multi-step predictions. We study this mismatch through two complementary regularization targets: marginal representation geometry and temporal error cancellation. We combine an anchored ellipsoidal extension of SIGReg with hierarchical rollout gaps (HGap). The ellipsoidal term allows directional target variances while retaining an isotropic anchor. HGap decomposes rollout error into differences between hybrid trajectories of the current model, then penalizes cancellation between groups of these contributions. We characterize the resulting hierarchy of upper bounds in a shared positive-definite metric. Across four visual control tasks, the combined method achieves a mean success rate of 85.50%, compared with 79.25% for our LeWM reproduction, an improvement of 6.25 percentage points. These rates average six evaluation seeds for one trained model per task. Separate component studies examine geometry regularization and frozen-geometry adaptation under their respective protocols. Anchored ellipsoidal regularization achieves a mean success rate of 84.17%. With visual representations frozen, HGap adaptation improves mean success from 43.75% to 47.19% at long horizons and from 81.13% to 82.56% at short horizons. The framework combines directional representation regularization with an explicit measure of temporal error cancellation in a common prediction objective.