Reward-Oracle MCTS for Formal Theorem Proving: Sample-Efficient Search and the Need for Kernel-Level Proof Auditing

arXiv cs.AISeptember 1, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2608.28639v1 Announce Type: new Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existing tree search approaches either feed verbose compiler error messages directly into the generation context, increasing context usage during search, or employ non-standard evaluation protocols that prevent direct comparison with established baselines. We propose a three-role Monte Carlo Tree Search (MCTS) framework that treats the Lean 4 compiler purely as a reward oracle using compiler output as a scalar signal for UCB-guided tree updates without feeding error content into the generation context.

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