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

2026-06-27

AI Summary

This work addresses the challenge of unifying prediction, planning, and irreversibility within world models. It formulates prediction as a probability measure over future trajectories and, under a local Markov assumption, employs the Onsager–Machlup action functional to decompose latent dynamics into reversible and irreversible components in path space. The authors introduce rollout-based entropy production as an operational measure of irreversibility. Through path-integral analysis, attention mechanism inspection, and small-scale model experiments, they find that attention asymmetry emerges in response to increasing data irreversibility. While symmetrization interventions suppress entropy production, they selectively impair long-horizon prediction of irreversible processes yet preserve the model’s capacity to capture relaxation dynamics.

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.

Problem

• world models
• prediction
• irreversibility
• path-space
• entropy production

Innovation

• path-space formulation
• Onsager-Machlup action
• irreversibility
• entropy production
• world models