LeAct Teaches Models to Reason from Expert Actions.

Modern reasoning models heavily rely on explicit reasoning data, typically sourced from human annotations or distilled from powerful large language models. However, a vast and underexploited resource exists in expert systems, such as game engines or theorem provers, which consistently produce near-optimal actions but do not articulate their underlying thought processes. This research introduces LeAct (Learning to reason from Actions), a novel approach designed to recover these latent "chains of thought" (CoT) from expert actions alone. LeAct treats the CoT as a latent variable and optimizes it by having the student model sample candidate CoTs for each expert action. It then retains only those CoTs that demonstrably improve the student's probability of reproducing the expert's action. This method effectively distills expert knowledge into a student model, enabling it to generalize beyond mere action imitation. Evaluations across various imperfect-information games and a simulated robotics benchmark show LeAct's effectiveness. It reaches the numerical performance floor on smaller enumerable games and significantly outperforms strong expert-iteration baselines on larger scales, including winning head-to-head in Flop Hold'em. On the robotics probe, LeAct was the only training recipe to improve upon direct imitation, establishing expert systems as a new, powerful source of reasoning teachers for foundation models.