Algebraic World Model: From Exploration to Proofs
AWM produced Lean-checked proofs ruling out every winning sequence on two impossible game levels in all six runs.
The framework learns unfamiliar environments by testing and revising executable Python hypotheses, then formalizes its models in Lean 4. The authors report that coding-equipped Claude Opus 5.5 and GPT-6 Astra produced no impossibility proofs across twelve baseline runs. AWM initially found four of six correct bounds; feedback that a cheaper win existed prompted revised rules and proofs, bringing it to six of six. Across 25 public ARC-AGI-3 games, its models also let Lean replay winning trajectories for all 183 levels.
ArXiv · AI/CL/LG's note
The framework learns unfamiliar environments by testing and revising executable Python hypotheses, then formalizes its models in Lean 4. The authors report that coding-equipped Claude Opus 5.5 and GPT-6 Astra produced no impossibility proofs across twelve baseline runs. AWM initially found four of six correct bounds; feedback that a cheaper win existed prompted revised rules and proofs, bringing it to six of six. Across 25 public ARC-AGI-3 games, its models also let Lean replay winning trajectories for all 183 levels.
ArXiv · AI/CL/LG's note
score 5