Kimina-Prover - A mathematical theorem proof model jointly launched by the Dark Side of the Moon and Numina
Kimina-Prover is a large-scale mathematical theorem proving model developed in collaboration between the Dark Side of the Moon and the Numina team. The model is trained using large-scale reinforcement learning and can reason in a human-like manner, providing rigorous proofs in the Lean 4 language...
What is Kimina-Prover?
Kimina-Prover is a large-scale mathematical theorem proving model developed in collaboration between Lunar Dark Side and the Numina team. Trained using large-scale reinforcement learning, the model can reason in a human-like manner, rigorously proving mathematical theorems in the Lean 4 language. Through a unique "formal reasoning mode," it interweaves informal reasoning and Lean 4 code snippets during the reasoning process, simulating human problem-solving strategies. Kimina-Prover achieved a score of 80.7% on the miniF2F benchmark, exceeding the previous best by 10.6%, setting a new record. Performance significantly improves with increasing model size and computational resources, demonstrating high sample efficiency and good scalability. Versions with 1.5B and 7B parameters are open-source.
Kimina-Prover's main functions
- Based on reinforcement learningKimina-Prover is the first large-scale formal reasoning model trained through massive reinforcement learning, capable of reasoning in a human-like manner and rigorously proving mathematical theorems in the Lean 4 language.
- Efficient reasoning modeThe model employs a structured reasoning model called "formal reasoning mode," which incorporates informal reasoning and relevant Lean 4 code snippets into the reasoning process, enabling the model to better simulate human problem-solving strategies.
- High sample efficiencyKimina-Prover achieves good results with fewer samplings, and its performance improves significantly with increased computing resources.
- Model size and performance are positively correlatedUnlike previous neural theorem provers, Kimina-Prover's performance improves significantly with increasing model size.
Kimina-Prover's Technical Principles
- Automatic formalizationTo construct a diverse set of questions, the researchers trained a model that automatically translates natural language question statements into Lean 4 code and ends with placeholder proofs.
- Reinforcement learning trainingFollowing the Supervised Fine-Tuning (SFT) phase, the model further enhances its formal theorem-proving capabilities through reinforcement learning. In each iteration, the model samples a batch of problems from the problem set and generates multiple candidate solutions, then uses the Lean compiler to verify the correctness of these solutions.
Kimina-Prover's performance
- Benchmark scoresIn the miniF2F benchmark test, Kimina-Prover achieved a score of 80.7%, surpassing the previous state-of-the-art (SOTA) model by 10.6%, setting a new record.
- Comparison with general large modelIn miniF2F benchmarks and subsets such as IMO and AIME, Kimina-Prover significantly outperforms general inference models such as OpenAI’s o3 and Gemini 2.5 Pro.
Kimina-Prover's project address
- Github repository:https://github.com/MoonshotAI/Kimina-Prover-Preview/tree/master
- HuggingFace model library:https://huggingface.co/collections/AI-MO/kimina-prover-preview
- arXiv technical paper:https://arxiv.org/pdf/2504.11354
Application scenarios of Kimina-Prover
- Research supportKimina-Prover has enormous application potential in the field of mathematical research. It can help mathematicians and researchers quickly verify complex mathematical theorems and provide rigorous proof processes.
- Software testingIn the software development process, Kimina-Prover can be used to verify the logical correctness of the software. By converting the software's algorithms and logic into the form of mathematical theorems, the model can verify the correctness of these theorems, ensuring the reliability and stability of the software.
- Algorithm verificationIn the fields of artificial intelligence and machine learning, Kimina-Prover can be used to verify the correctness and reliability of algorithms, ensuring that they are theoretically correct.
- risk assessmentIn the financial field, Kimina-Prover can be used to validate the mathematical foundations of risk assessment models, ensuring the accuracy and reliability of these models.
- Engineering design verificationIn engineering design, Kimina-Prover can be used to verify mathematical models and formulas used in designs. In fields such as architectural structural design and mechanical design, the model can verify the stability and safety of the design.