# Order-Consistent Latent Geometry for Reliable Short-Horizon Planning in World Models

arXiv: https://arxiv.org/abs/2610.18570 · HTML: https://mlsanity.com/paper/2610.18570/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 12 of 12)

- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [Learning Plannable Representations with Causal InfoGAN](https://mlsanity.com/paper/1807.09341/) (2018)
- [Temporal Straightening for Latent Planning](https://mlsanity.com/paper/2603.12231/) (2026)
- [Deep Value Model Predictive Control](https://mlsanity.com/paper/1910.03358/) (2019)
- [Predictive but Not Plannable: RC-aux for Latent World Models](https://mlsanity.com/paper/2605.07278/) (2026)
- [Self-Approaching Graphs](https://mlsanity.com/paper/1306.5460/) (2013)
- [Learning The Minimum Action Distance](https://mlsanity.com/paper/2506.09276/) (2025)

## 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.