Latent Dynamics · 2026-10-14
Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models
Junlin Wu, Wen Fan, Dandan Zhang
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
The authors study latent goal planning that scores action candidates by terminal Euclidean distance in latent space. They show that preserving the correct ordering of true progress along transition-shortest rollouts is equivalent to the classical self-approaching condition. For polygonal (discrete) world-model rollouts, an acute bend can create a region where terminal Euclidean scoring prefers a transition-worse candidate. They validate the ordering failure with a controlled six-branch experiment and interpret latent dimension via an angular-capacity bound.
Why it matters
Even with exact latent rollouts, terminal Euclidean goal matching can select an action that moves the wrong way if latent geometry allows “progress reversal” for short-horizon lookahead. The paper provides a concrete compatibility condition (self-approachingness) for reliable terminal-distance guidance, and identifies when acute geometry in visual world models leads to exact finite-horizon candidate-order inversions.
Method
- Define pathwise transition-order consistency for transition-shortest rollouts, requiring that latent distance does not reverse progress along the rollout (equivalent to self-approachingness).
- Model visual world models’ discrete latent sequences via polygonal interpolation; prove a sharp non-acute criterion and derive an exact finite-horizon candidate-order reversal under acute bends.
- Run a controlled six-branch star experiment using (i) 2D regular hexagon, (ii) zero-padded 3D hexagon, and (iii) a 3D cross-polytope; compare misranking and closed-loop success across planning horizons.
Limitation
The authors state their guarantees are pathwise and apply to graph-like point bottlenecks with locally reversible branches; they do not ensure global ranking across unrelated paths or imply impossibility for continuous-action tasks.
Abstract (from arXiv)
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.
Related papers
- Latent World Models Should Plan with Distances Along the Latent Manifold
- How Long, Not How Close: A Learned Temporal Metric for Planning in Latent World Models
- Beyond a single latent space: a dual-latent world model for long-horizon planning
- Control-Geometry Straightening for Sampling-Based Latent Planning
- ATLAS: Aligned Transport of Latent Structure for Reliable World Model Planning
Publication record
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First public release: 2026-10-13 · Indexed by Pub-AI: 2026-10-14 UTC
Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models
Preprint posted: 2026-10-13 · Original record ↗
- arxiv
- 2610.18570
Explicit source versions (1)
- v1 · 2026-10-13
- Preprint available
Source date: 2026-10-13 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
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.