Learning Commute-Time-Preserving World Models for Planning
CTWMs learn commute-time-preserving latents for planning and match LeWM with half the parameters.
The paper argues that latent planning improves when distances mirror commute times from a correctly scaled graph-Laplacian spectral embedding. Common self-supervised objectives that encourage isotropic representations can degrade that eigenvalue-dependent scaling. Commute-Time-Preserving World Models pair a latent displacement predictor with a log-determinant regularizer that prevents collapse and, under reversible deterministic dynamics, recover the scaled Laplacian at the predictor's fixed point. In simulations, CTWM matches or outperforms LeWM on continuous goal-reaching benchmarks while using half the parameters.
- Isotropic self-supervised objectives can distort eigenvalue-dependent commute-time scaling.
- CTWM combines a latent displacement predictor with a log-determinant regularizer.
- At the fixed point it recovers correctly scaled Laplacian embeddings under stated dynamics.
- CTWM matches or beats LeWM on goal-reaching tasks using half the parameters.
From the original article
1 min read at arxiv.orgWorld 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.
By Michael Hauri · arxiv.org
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