Diffusion-Proof: Recipe for Formal Theorem Proving Beyond Auto-Regressive Generation
Diffusion-Proof framework uses dLLMs for formal theorem proving, achieving a 6.14% improvement over AR models.
Key Findings
Methodology
The Diffusion-Proof framework integrates dLLM-Prover-7B for whole-proof writing and dLLM-Corrector-7B for local correction. Through large-block diffusion training, the models excel in long-range coherence and bidirectional information utilization.
Key Results
- Diffusion-Proof achieves 50.00% accuracy on MiniF2F-Test, a 6.14% improvement over the baseline. It also shows a 1.61% improvement on ProofNet-Test.
- Diffusion-Proof successfully solves an IMO problem that more advanced models could not, highlighting its advantage in complex reasoning.
- Validation loss study shows dLLM outperforms AR models in causal attention loss, especially in long-range coherence.
Significance
Diffusion-Proof demonstrates the potential of diffusion models in formal theorem proving, particularly in long-range coherence and local correction. It not only enhances mathematical reasoning accuracy but also opens new avenues for applying large language models in formal domains.
Technical Contribution
Diffusion-Proof is the first framework to apply dLLMs to formal theorem proving, introducing a large-block correction training method that significantly enhances long-range coherence and bidirectional information utilization.
Novelty
Diffusion-Proof is the first framework to apply dLLMs in formal theorem proving, overcoming AR models' limitations in long-range coherence and local correction.
Limitations
- On the ProofNet-Test, the corrector module shows no significant improvement, indicating limitations in complex knowledge domains.
- The model may require more complex training data for handling advanced mathematical concepts.
Future Work
Future work could explore applications in more complex mathematical domains, optimize the corrector module's performance in complex knowledge areas, and expand to other formal languages.
AI Executive Summary
Enhancing the formal mathematical reasoning capabilities of large language models has become a key focus in recent research. Traditional autoregressive models face significant limitations in long-range coherence and error accumulation. The Diffusion-Proof framework introduces diffusion models to formal theorem proving, demonstrating advantages in long-range coherence and local correction.
The Diffusion-Proof framework includes two models: dLLM-Prover-7B for whole-proof writing and dLLM-Corrector-7B for local correction. Through large-block diffusion training, the models utilize bidirectional information for local correction, significantly improving mathematical reasoning accuracy.
Experimental results show that Diffusion-Proof achieves 50.00% accuracy on the MiniF2F-Test, a 6.14% improvement over the baseline. It also shows a 1.61% improvement on the ProofNet-Test. Notably, Diffusion-Proof successfully solves an IMO problem that more advanced models could not, highlighting its advantage in complex reasoning.
Deep Dive
Abstract
Enhancing the formal math reasoning capabilities of Large Language Models (LLMs) has become a key focus in both mathematical and computer science communities in recent years. While significant progress has been made in using state-of-the-art Auto-Regressive (AR) LLMs for formal theorem proving, these models suffer from inherent limitations. Their next-token prediction generation methods may yield suboptimal performance due to the challenges of long-range coherence and the compounding of errors over long sequences. Recent advancements in diffusion LLMs (dLLMs), which generate text through iterative denoising of a multi-token block, offer a promising alternative. However, the application of dLLMs to formal mathematics, where maintaining long-range coherence is critical, remains largely understudied. To address the challenges above, we propose **Diffusion-Proof**, to the best of our knowledge, the first framework to train and apply dLLMs for formal theorem proving. Our frameworks contain training and inference methods for two models. The first one is *dLLM-Prover-7B*, which performs whole-proof writing with long-range coherent tactic usage. The second one is *dLLM-Corrector-7B*, which is a novel large block diffusion-based correction model. It leverages the in-filling capabilities of dLLMs to perform local proof correction using bi-directional information. Extensive experiments demonstrate that **Diffusion-Proof** relatively significantly outperforms the AR LLM baseline trained under the same dataset. **Diffusion-Proof** achieves an absolute improvement of **1.61%** on ProofNet-Test and **6.14%** on MiniF2F-Test benchmarks compare to the baseline. Notably, **Diffusion-Proof** successfully resolves one IMO problem that more advanced thinking model DeepSeek-Prover-V2-7B could not solve, showcasing the unique advantage of dLLMs in formal theorem proving.