A Path-Space Formulation of Prediction in World Models: From a Single Action to Prediction, Planning, and Irreversibility

• URL: http://arxiv.org/abs/2606.28751v1
• Date: Sat, 27 Jun 2026 06:00:09 GMT
• Title: A Path-Space Formulation of Prediction in World Models: From a Single Action to Prediction, Planning, and Irreversibility
• Abstract summary: We propose a path-space formulation of prediction in AI world models.<n>We decompose latent dynamics into reversible and irreversible components.<n>We find that attention asymmetry is acquired during training in proportion to the irreversibility of the data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a path-space formulation of prediction in AI world models. Rather than sequences of one-step conditional distributions, we argue that a world model implicitly defines a probability measure over future trajectories. In the local regime where latent dynamics admit an effective Markovian description, this path measure takes the Onsager-Machlup form. Within this framework, prediction (most probable trajectory), planning (constrained optimization), and uncertainty (fluctuations) emerge as operations on a single action functional. We decompose the latent dynamics into reversible and irreversible components and introduce operational measures of entropy production from model rollouts. In controlled small-scale attention-based models, we find that attention asymmetry is acquired during training in proportion to the irreversibility of the data. Symmetrizing the learned attention suppresses entropy production and selectively degrades long-horizon prediction of irreversible dynamics while preserving relaxational prediction. These results suggest that irreversibility may serve as a computational resource for predictive world models. More generally, the fundamental predictive object is a distribution over future paths rather than states.

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