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Goedel-Prover-V2 - A theorem proving model jointly open-sourced by Princeton University, Tsinghua University, and others.

Goedel-Prover-V2 is an open-source theorem prover jointly developed by top institutions such as Princeton University, Tsinghua University, and NVIDIA. Goedel-Prover-V2 utilizes hierarchical data synthesis, verifier-guided self-correction, and model...

What is Goedel-Prover-V2?

Goedel-Prover-V2 is an open-source theorem prover jointly developed by top institutions such as Princeton University, Tsinghua University, and NVIDIA. Goedel-Prover-V2 significantly improves the performance of automated formal proof generation through innovative techniques such as hierarchical data synthesis, verifier-guided self-correction, and model averaging. The model includes two parameter versions: 32B and 8B. The 32B model achieves a 90.4% pass@32 score in the MiniF2F benchmark, surpassing the 671B DeepSeek-Prover-V2. Goedel-Prover-V2 ranks first in PutnamBench and MathOlympiadBench benchmarks, demonstrating its powerful theorem proving capabilities. The release of Goedel-Prover-V2 represents a new milestone in AI research in the field of mathematical theorem proving.

Main functions of Goedel-Prover-V2

  • Automatically generate proofGenerate formal proofs for complex mathematical problems.
  • Self-correction abilityThrough feedback from the Lean compiler, the model can iteratively revise its proofs, thereby improving the quality of the proofs.
  • High-efficiency training and optimization: Improve training efficiency and model performance by using hierarchical data synthesis and model averaging techniques.
  • Open source and scalabilityIt provides open-source models and datasets to facilitate further development and improvement by researchers.

The technical principles of Goedel-Prover-V2

  • Scaffolded Data SynthesisIt automatically generates proof tasks of progressively increasing difficulty, helping the model gradually transition from simple to complex problems. By generating intermediate-difficulty problems, it fills the gap between simple and complex problems, providing a denser training signal.
  • Verifier-Guided Self-CorrectionThe model uses feedback from the Lean compiler to learn how to iteratively revise its proofs. It highly simulates the human process of refining proofs, improving their accuracy and reliability.
  • Model AveragingBased on the average of multiple training phases of model checkpoints, it restores model diversity. It significantly improves the overall model performance and enhances robustness at larger Pass@K values.

Performance of Goedel-Prover-V2

  • MiniF2F Benchmarking:
    • 32B model:
      • Pass@32The accuracy reached 90.4%, which is significantly better than DeepSeek-Prover-V2-671B's 82.4%.
      • Self-calibration modeIn self-calibration mode, the Pass@32 score further improved to 90.4%.
    • 8B model:
      • Pass@32The accuracy rate reached 83.3%, comparable to DeepSeek-Prover-V2-671B's 82.4%, but the model size was nearly 100 times smaller.
  • PutnamBench benchmark:
    • 32B model:
      • Pass@64It solved 64 problems, ranking first.
      • Pass@32It solved 57 problems, significantly outperforming DeepSeek-Prover-V2-671B's 47 problems.
    • 8B model:
      • Pass@32Its performance is also excellent, comparable to DeepSeek-Prover-V2-671B.
  • MathOlympiadBench benchmark:
    • 32B modelIt solved 73 problems, significantly outperforming DeepSeek-Prover-V2-671B's 50 problems.
    • 8B modelThe results are also very close, demonstrating a strong ability to prove theorems.

Goedel-Prover-V2 project address

  • Project official websitehttps://blog.goedel-prover.com/
  • HuggingFace model library:
    • https://huggingface.co/Goedel-LM/Goedel-Prover-V2-8B
    • https://huggingface.co/Goedel-LM/Goedel-Prover-V2-32B

Application scenarios of Goedel-Prover-V2

  • Mathematical theorem proofIt automatically generates formal proofs of mathematical theorems, helping mathematicians verify conjectures, explore new mathematical theories, and accelerate the process of mathematical research.
  • Software and hardware verificationIn software development and hardware design, it verifies the correctness of algorithms, program logic, and circuit designs. Formal proofs ensure the reliability of software and hardware systems, reduce errors and vulnerabilities, and improve system security.
  • educateAs an auxiliary tool for mathematics education, it provides students with examples of formal proofs to help them better understand and master mathematical concepts and theorems.
  • Artificial intelligence and machine learningIn the fields of artificial intelligence and machine learning, the mathematical foundations and algorithmic logic of models are verified to ensure their reliability and accuracy.
  • Scientific Research and Engineering: To verify mathematical models and theories in scientific research, helping scientists and engineers ensure the feasibility and reliability of design solutions.
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