Source
Richens, Abel, Bellot and Everitt (2025), LIT-1891, §§2.5, 3, 5 and footnote 1 (pp. 4–8); read in NOTE-1469. The lookup table is Block’s (LIT-642, THEORY-092).
What was actually shown
What “contains” means. “The existence of this algorithm, which converts π into a bounded error world model, implies the world model is encoded in the agent’s policy, and learning such policy is informationally equivalent to learning a world model” (p. 5). The world model is “any approximation P̂ of the transition function” (p. 4). It is the environment’s, not the agent’s subjective model.
Not a free attribution. Representation theorems fit beliefs and a utility to any coherent policy: “we may be able to assign a specific world model and utility function to a purely random policy … but this clearly does not imply that learning a world model is necessary” (p. 8). Theorem 1’s P̂ is fixed by the policy to within its error bound (THEORY-1249). Two observers with different priors cannot read off different transition functions. So within the theorem’s scope, ascribing a world model is not a choice of stance in the way Orseau et al.’s agent-or-device verdict is prior-relative (THEORY-624).
Not a mechanism. The map is “from the agent’s policy rather than its activations. This is strictly weaker (as the policy is a function of the activations)” (p. 7). The theorem holds “regardless of the details of its training and architecture” (p. 2), and “proves the existence of a world model encoded in the agent’s policy, not its specific use” (p. 7). The authors decline the interventional criterion used in interpretability as “tantamount to assuming the agent has a causal world model to begin with” (footnote 1, p. 8).
The corollary. Def. 5 constrains only the map (h, ψ) ↦ a. A table that stores a δ-bounded agent’s choice for every history and goal of depth ≤ n is itself δ-bounded, and Algorithm 1 returns the same P̂ from it. By the paper’s definition the table contains a world model. Nothing in the theorem distinguishes it from a planner with an explicit model.
What this does not say
- That the attribution is “merely explanatory”. It is a determinate property of the goal-conditioned behavioural disposition, though not of any finite record of behaviour: the queries are counterfactual goals at s₀, which a single run does not show.
- That a table is a realistic implementation. It grows with the number of histories and goals. Whether every implementation of a δ-bounded policy over a rich goal family must spend resources close to those of P itself, or must contain a separable predictive part, is not addressed. That is the open compression question.
- That interventions are uninformative. The paper avoids them as a criterion; it does not show they could not locate a model in a given agent.
- Anything beyond its scope. Full observation, finite stationary communicating environments, deterministic policies (THEORY-1249).