Compile to Compress: Boosting Formal Theorem Provers by Compiler Outputs
Summary: arXiv:2604.18587v1 Announce Type: cross
Abstract: Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this work, we address this scalability bottleneck by exploiting an informative structure in formal verification: the observation that compilers map a vast space of diverse proof attempts to a compact set of structured failure modes.
We introduce a learning-to-refine framework that leverages this compression to perform efficient learning and proof exploration. We perform tree search that corrects errors locally conditioned on explicit verifier feedback, thereby circumventing the costs associated with accumulating a long history of proof attempts. Extensive evaluations show that our method consistently amplifies the reasoning capabilities of base provers across varying scales.
Notably, our approach achieves state-of-the-art performance on PutnamBench among publicly reported ~8B and ~32B parameter models under comparable test-time budgets, offering a scalable paradigm for next-generation verifier-guided reasoning.
Key Contributions
- Scalability Improvement: The proposed method addresses scalability issues inherent in existing formal theorem provers, allowing for more efficient computations without the need for extensive resources.
- Learning-to-Refine Framework: By introducing a framework that focuses on local error correction based on immediate feedback, the approach minimizes the reliance on lengthy historical data of proof attempts.
- Tree Search Methodology: The implementation of a tree search mechanism enables targeted error correction, enhancing the overall proof exploration process.
- Performance Benchmarking: The approach has been rigorously evaluated against established benchmarks, demonstrating superior performance in comparison to leading models.
Implications for Future Research
The findings in this work pave the way for further research into the optimization of formal theorem proving frameworks. Potential areas for exploration include:
- Integration of additional machine learning techniques to further improve the learning-to-refine framework.
- Investigation of alternative compilers and their mappings to structured failure modes to enhance the robustness of the proposed method.
- Expansion of the approach to other forms of automated reasoning beyond formal theorem proving.
- Collaborative studies to benchmark against more diverse datasets, ensuring the generalizability of the proposed solutions.
Conclusion
In conclusion, the research presents a promising approach to overcoming the scalability challenges faced by formal theorem provers through innovative compression techniques derived from compiler outputs. By effectively utilizing structured failure modes, the proposed framework not only enhances the performance of existing models but also sets a precedent for future advancements in automated reasoning systems.