CTWM world models preserve commute-time structure for planning with half the parameters
hisspikeness · x · 2026-10-05
Hauri, Zenke et al. published 'Learning Commute-Time-Preserving World Models for Planning' on arXiv.
Core idea: agents plan in latent space by minimizing distance to goals, so latent distances that mirror the environment's commute-time structure help planning. Spectral embeddings of the graph Laplacian have this property, but building the Laplacian is intractable in large continuous environments, so self-supervised learning is needed.
Key findings and method:
- Existing methods commonly encourage isotropic representations to prevent collapse, which degrades the eigenvalue-dependent scaling of the spectral embedding and distorts commute times
- CTWM combines a latent displacement predictor with a log-determinant regularizer that provably recovers the correctly scaled Laplacian representation under reversible deterministic dynamics
- CTWM matches or outperforms the task-agnostic baseline LeWM on several continuous goal-reaching benchmarks with half the parameters
- The authors visualize PointMaze: CTWM's latent distances track true commute-time structure near bottlenecks far better than LeWM
Paper, code, and project page are public.
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