# Learning Commute-Time-Preserving World Models for Planning

arXiv: https://arxiv.org/abs/2610.01373 · HTML: https://mlsanity.com/paper/2610.01373/

## 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 22 of its 70 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [The Laplacian in RL: Learning Representations with Efficient Approximations](https://mlsanity.com/paper/1810.04586/) (2018)
- [Temporal Straightening for Latent Planning](https://mlsanity.com/paper/2603.12231/) (2026)
- [Temporal Difference Flows](https://mlsanity.com/paper/2503.09817/) (2025)
- [stable-worldmodel: A Platform for Reproducible World Modeling Research and Evaluation](https://mlsanity.com/paper/2605.21800/) (2026)
- [Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models](https://mlsanity.com/paper/2605.09241/) (2026)
- [Variance-Covariance Regularization Improves Representation Learning](https://mlsanity.com/paper/2306.13292/) (2023)
- [Reachability-Aware Laplacian Representation in Reinforcement Learning](https://mlsanity.com/paper/2210.13153/) (2022)
- [Multistep Quasimetric Learning for Scalable Goal-conditioned Reinforcement Learning](https://mlsanity.com/paper/2511.07730/) (2025)
- [Compositional Planning with Jumpy World Models](https://mlsanity.com/paper/2602.19634/) (2026)
- [Laplacian Representations for Decision-Time Planning](https://mlsanity.com/paper/2602.05031/) (2026)
- [Understanding Self-Supervised Learning via Latent Distribution Matching](https://mlsanity.com/paper/2605.03517/) (2026)
- [Dreamer-CDP: Improving Reconstruction-free World Models Via Continuous Deterministic Representation Prediction](https://mlsanity.com/paper/2603.07083/) (2026)

## Abstract (arXiv)

World models allow agents to plan in latent space by choosing a sequence of actions that most reduces the distance to a given goal state. Thus, planning can benefit from latent representations whose distances mirror commute-times in the environment. The spectral embedding space of the graph Laplacian provides such a representation, if it obeys a specific eigenvalue-dependent scaling. Unfortunately, instantiating the graph Laplacian is intractable in large, continuous environments. Self-supervised learning offers a natural route to such commute-time-preserving embeddings at scale. However, here we show that existing methods, which commonly encourage isotropic representations to prevent representational collapse, tend to degrade the "correct" eigenvalue-dependent scaling, leading to an inaccurate representation of commute times. To address this problem, we introduce Commute-Time-Preserving World Models (CTWMs), combining a latent displacement predictor and a log-determinant regularizer that prevents collapse, which provably recover the correctly scaled Laplacian representation under reversible deterministic dynamics and at the predictor's fixed point. In numerical simulations, CTWM matches or outperforms LeWM, a task-agnostic baseline, on several complex, continuous goal-reaching benchmarks, while using half the parameters.