Abstract Beliefs for Code World Models

Code world models represent environment dynamics as executable programs. Under partial observability, existing methods maintain beliefs with concrete particles, each committing every hidden variable to a single value. As joint assignments grow combinatorially with the number of hidden variables, covering the plausible states exhausts a fixed particle budget. We introduce the distributional particle (d-particle), whose state variables can each hold a distribution over possible values, so one particle can represent many possible worlds. Building on d-particles, we propose Abstract Belief Coder (ABC): a shared Factor Library defines distribution families whose operations propagate and condition these distributions and return the likelihoods that weight particles, and an LLM proposes state representations and programs ranked by this filtering likelihood. On six partially observed MiniGrid tasks, ABC succeeds in 90.6% with ground-truth models versus 55.0% for a concrete-particle baseline, and in 75.6% versus 46.1% with LLM-generated models; it also leads on two Crafter tasks.