What a World Model Represents Is Three Questions

Abstract

World models learn task-relevant information through many routes: observation reconstruction, recurrent state, temporal filtering, and explicit task supervision. Different routes can make different variables available. The same variable can also be available through several routes at once. When it is, looking at which route would increase the training loss most if removed does not tell you which route the model actually uses. The questions are reachability, whether a training signal can identify a task-relevant direction; admission, whether that direction is recoverable from the latent; and assignment, which eligible route carries it. We test them in environments with a known set of required coordinates. A direction cannot enter the latent unless some training signal can identify it. Reconstruction, recurrence, or filtering may already recover some of those coordinates; a reward or value head then has no residual direction to admit. For what remains, how many independent predictions the target supplies is how many coordinates install: one through four independent predictions admit one through four directions, including through the value head. Reachability is not admission: a temporal second-moment coefficient can remain absent under next-token prediction when accumulating it is a fraction of a percent of that loss, and a head that predicts the coefficient restores it. Assignment is a different test. Two routes that each carry the same variable when trained alone do not swap the carrier when we reverse which is more costly to remove. A recurrent model trained on a transformer's recorded sequences shows the same pattern. Near the point where the competing route is beginning to clear the probe threshold, independent training runs disagree. What a world model represents is therefore three questions: what information is reachable, what supervision admits, and which competing route carries it.

24 pages, 12 figures. Substantial rewrite of v1 (title changed). v2 Adds the reachability / admission / assignment split and the assignment experiments / the route-boundary / RSSM-transfer / stochastic-onset and reachability-versus-admission experiments