Counterexample Generation via Per-Theorem Symbolic Verifiers: When Imitation Hurts and Reinforcement Repairs
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Abstract
The paper discusses the challenges of counterexample generation in theorem proving and presents a new training environment called SymCE, which improves model performance in recognizing true theorems.
Reality Card
The introduction of reinforcement learning with a sparse reward function significantly improves the model's ability to recognize true theorems, achieving a recognition score of 0.66 compared to 0.00 with counterexample-only supervised fine-tuning.
The model outperformed every evaluated 7B open-weights math specialist and achieved a 97.7% accuracy in human audits of verifier decisions.
The study's findings may not generalize across different model architectures or larger datasets, raising concerns about reproducibility.
Paper to code
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