Learn from Failure: Fine-Tuning LLMs with Trial-and-Error Data for Intuitionistic Propositional Logic Proving

Understand

Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e.

• proof steps) to search through proof states.
• The current model, while trained solely on successful proof paths, faces a discrepancy at the inference stage, as it must sample and try various tactics at each proof state until finding success, unlike its training which does not incorporate learning from failed attempts.
• Intuitively, a tactic that leads to a failed search path would indicate that similar tactics should receive less attention during the following trials.