Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models
Latent planners often rank candidate action sequences by terminal Euclidean distance to a goal latent.
ProofPaper ↗
Key points
- 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.
Sources (1)
- [1]Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World ModelsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 03:38 PM
Latent planners often rank candidate action sequences by terminal Euclidean distance to a goal latent.
We show that this pathwise no-reversal requirement is precisely the classical self-approaching condition.
Extractive summary: sentences quoted from the sources.
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