Latent planners often rank candidate action sequences by terminal Euclidean distance to a goal latent. Exact agreement with transition distance would make this score ideal, but is stronger than planning requires: along a transition-shortest rollout, the essential requirement is that latent distance does not reverse true transition progress. We show that this pathwise no-reversal requirement is precisely the classical self-approaching condition. To the best of our knowledge, we are the first to identify self-approachingness as a planner-facing compatibility condition for terminal Euclidean latent planning and to connect its violation to an exact finite-horizon candidate-order reversal. Because visual world models predict discrete latent sequences, we analyze their polygonal interpolation. We prove that an acute bend creates a nonempty region in which terminal Euclidean distance ranks a transition-worse candidate ahead of one that makes genuine progress, even under exact rollouts. We further interpret latent dimension as angular capacity through a classical spherical-code bound. A controlled six-branch experiment, including a zero-padded three-dimensional baseline, validates the predicted ordering failure and separates angular arrangement from ambient dimensionality.
Figures & tables
Figure 1: Geometry of the six-branch latent embeddings. (a) A two-dimensional regular hexagon, in which adjacent branch directions form acute angles. (b) A three-dimensional zero-padded copy of the same hexagon, which changes the ambient dimension but preserves all pairwise angles. (c) A three-dimensional cross-polytope embedding with directions {±e1,±e2,±e3} , in which all branch pairs are non-acute. The comparison separates angular arrangement from ambient dimension alone.
Figure 2: (a) Strict terminal-score misranking across planning horizons. (b) Receding-horizon planning success. All three embedding conditions are plotted. The 2D and zero-padded 3D hexagons overlap exactly because zero-padding preserves their pairwise angular geometry. Only the reoriented 3D cross-polytope removes acute conflicts, strict misrankings, and the associated planning failures.
Latent world models plan by rolling a frozen predictor forward under candidate action sequences and ranking the candidates by the latent distance between their imagined end state and the goal. However, this ranking breaks down when the goal lies several plans away, because the latent distance measures how closely an end state resembles the goal rather than how far it remains from reaching it. To address this, we propose TEMPO, a temporal-distance planning objective that leaves the world model untouched, learns only from the recorded trajectories already used to train it, and adds negligible cost to the planner's search. TEMPO learns a small map of the frozen latent in which the distance between two states of an episode reflects the number of environment steps between them, and blends this distance into the planner's cost. It requires no rewards, policies or success labels and, being a cost rather than a model, applies to frozen world models with one latent vector per state that plan by a latent distance. We evaluate TEMPO on eleven simulated environments (e.g., maze navigation, tabletop pushing, robotic arm control and three-dimensional manipulation) with the LeWM and PLDM planners. With a small MLP that adds at most 0.3% to a plan's arithmetic, TEMPO improves both planners at every goal distance, including the one-plan setting of their evaluations, raises LeWM from 36% to 99% on TwoRoom three plans from the goal, and remains competitive on a broad range of 2D and 3D navigation, reaching and manipulation tasks.
Learning good representations is essential for latent planning with world models. While pretrained visual encoders produce strong semantic visual features, they are not tailored to planning and contain information irrelevant -- or even detrimental -- to planning. Inspired by the perceptual straightening hypothesis in human visual processing, we introduce temporal straightening to improve representation learning for latent planning. Using a curvature regularizer that encourages locally straightened latent trajectories, we jointly learn an encoder and a predictor of a Joint-Embedding Predictive Architecture (JEPA) world model. We show that reducing curvature this way makes the Euclidean distance in latent space a better proxy for the geodesic distance and improves the conditioning of the planning objective. We demonstrate empirically that temporal straightening makes gradient-based planning more stable and yields significantly higher success rates across a suite of goal-reaching tasks. Our code is available at https://agenticlearning.ai/temporal-straightening.
Ying Wang, Oumayma Bounou, Gaoyue Zhou +4
New York University · Brown University · University of Toronto
Latent world models can learn representations that contain information needed for control, while the downstream controller may still rank candidate actions poorly when it relies on terminal latent distance alone. We study this failure in a fixed encoder and introduce trajectory reachability metrics (TRM), a small temporal pairwise cost trained from logged trajectories and used to rank predicted endpoints of a candidate action sequence against a goal. In the TwoRoom evaluation on 100 episodes from a high distance range, the original controller with LeWorldModel reaches 7.0% mean success. Temporal TRM trained after excluding all evaluation episodes reaches 96.7%, shuffled label controls stay at 0.0%, and TRM also improves PLDM from 32.7% to 84.0%. TopoNav, a separate pixel navigation task, shows the same link between repaired ranking and closed loop control. The selection audit with shared candidates (SASC) and rowspace interventions show that the gain comes from reweighting latent directions carrying the action decision. The XY rowspace contributes less than 1% of terminal latent MSE but carries most of the information needed for control. Coverage and boundary tests define the scope. Balanced doorway coverage restores a 0.0% coverage failure to 100.0% success, while an unseen wall orientation and contact rich PushT expose layout, dynamics, and recovery limits.