AI Research & Development
Unlocking Advanced Theorem Proving with BFS-Prover
The BFS-Prover system redefines automatic theorem proving (ATP) by demonstrating that Best-First Search (BFS), often considered suboptimal, can achieve state-of-the-art performance when strategically scaled. This breakthrough challenges conventional wisdom and opens new avenues for AI-driven mathematical reasoning.
Transforming Mathematical Reasoning with Scalable AI
BFS-Prover's innovative approach offers significant implications for industries reliant on formal verification and complex problem-solving. By simplifying the underlying search mechanism, it promises more accessible and efficient AI-powered solutions.
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MiniF2F Test Score
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Efficiency Gain (vs. MCTS)
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Computational Simplicity
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
BFS-Prover System
Expert Iteration Pipeline
Scalability & Performance
The BFS-Prover system leverages a length-normalized Best-First Tree Search (BFS) combined with a policy LLM, integrating LeanDojo for interactive theorem proving. This architecture enables efficient navigation of complex proof spaces.
Enterprise Process Flow
Proof State Update
→
Tactic Generation (LLM Policy)
→
LeanDojo Execution
→
Node Expansion
→
Proof Path Identified
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Optimal Alpha for Deep Path Exploration
BFS-Prover employs an iterative expert iteration pipeline to continually enhance the policy LLM's ability. It includes strategic data filtering, DPO from compiler feedback, and supervised fine-tuning to refine tactic generation.
| Feature | SFT Only | SFT + DPO |
|---|---|---|
| Training Data | Positive (proof paths) | Positive (proof paths) & Negative (compiler errors) |
| Sample Efficiency | Good | Improved (sharpens policy distribution) |
| Error Handling | Implicit | Explicit (learns from invalid tactics) |
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Expert Iteration Rounds for Peak Performance
The system's distributed infrastructure, utilizing Ray for parallel proof search across multiple machines, achieves near-linear scaling. This allows BFS-Prover to tackle large-scale formal theorem proving tasks efficiently.
| Prover System | Critic | Search Method | MiniF2F Score |
|---|---|---|---|
| DeepSeek-Prover-V1.5 | No | MCTS | 63.5% |
| InternLM2.5-StepProver | Yes | BFS | 65.9% |
| HunyuanProver | Yes | BFS | 68.4% |
| BFS-Prover (this work) | No | BFS | 72.95% (accumulative) |
BFS-Prover Outperforms MCTS in ATP
Despite the perceived necessity of complex MCTS and value functions, BFS-Prover demonstrates that a carefully scaled BFS system can achieve superior performance. This is achieved by focusing on strategic data filtering, direct preference optimization, and length normalization, leading to higher success rates without the added computational overhead of critic models.
Calculate Your AI-Driven Proof Efficiency Gain
Estimate the potential savings and reclaimed hours by integrating BFS-Prover's advanced theorem proving capabilities into your enterprise.
Roadmap to Enhanced Formal Verification
Our structured implementation roadmap ensures a smooth transition and integration of BFS-Prover into your existing formal systems and workflows.
Phase 1: Discovery & Customization
Initial assessment of your current ATP challenges, data landscape, and specific proof requirements. Customization of BFS-Prover's policy LLM and search parameters for optimal alignment with your domain.
Phase 2: Integration & Training
Seamless integration of BFS-Prover with your Lean4 environment and existing verification tools. Focused training on your proprietary datasets to enhance proof generation accuracy and efficiency.
Phase 3: Deployment & Optimization
Full deployment of the BFS-Prover system within your infrastructure. Continuous monitoring, performance tuning, and iterative refinement based on real-world feedback to maximize ROI and proof discovery rates.
Ready to Revolutionize Your Theorem Proving?
BFS-Prover offers a powerful, scalable, and efficient solution for complex mathematical reasoning. Partner with us to achieve new levels of formal verification and accelerate your research and development.
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