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This paper establishes a rigorous theoretical link between latent planning reliability and the classical self-approaching condition, proving that acute bends in visual world model trajectories can cause Euclidean distance metrics to rank inferior candidates higher. By validating these geometric failures through controlled experiments, the work provides critical insights for improving short-horizon action selection in learned world models without requiring exact transition distance matching.
Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models
arXiv:2610.18570v1 Announce Type: new Abstract: 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.
Abstract: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.
Artificial Intelligence (cs.AI)
arXiv:2610.18570 [cs.AI]
(or arXiv:2610.18570v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.18570 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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