Objective Dimensionality Dictates World Model's Representational Capacity

New research investigates how much task-relevant information a world model's latent representations actually capture. It challenges the assumption that model quality is inherent, arguing instead that the specific predictive coordinates a task needs, termed the "closure," are crucial. The study demonstrates that the dimensionality of the objective function used for training directly dictates how much of this closure a latent space represents. The findings indicate that a common scalar value signal, like a single reward, only installs a one-dimensional projection of a potentially multi-dimensional task closure. When the objective's dimensionality is increased, the model installs a corresponding number of predictive directions. This suggests that "value equivalence" is not an all-or-nothing concept but rather a dimensional one, with the single-reward objective representing its "rank-one corner."