What is Kimina-Prover
Kimina-Prover is a large-scale mathematical theorem proving model launched through collaboration between the Moonshot AI and Numina teams. The model is trained with large-scale reinforcement learning and can reason in a human-like manner, rigorously proving mathematical theorems in the Lean 4 language. Through a unique "formal reasoning mode," it intersperses informal reasoning and Lean 4 code snippets during the reasoning process, simulating human problem-solving strategies. Kimina-Prover achieved 80.7% on the miniF2F benchmark, exceeding the previous best level by 10.6% and setting a new high. Performance improves significantly as model size and computational resources increase, demonstrating high sample efficiency and good scalability. The 1.5B and 7B parameter versions of the model have been open-sourced.
Main features of Kimina-Prover
- Based on reinforcement learning: Kimina-Prover is the first large-scale formal reasoning model trained through large-scale reinforcement learning. It can reason in a human-like manner and rigorously prove mathematical theorems in the Lean 4 language.
- Efficient reasoning mode: The model adopts a structured reasoning mode called "formal reasoning mode." By interspersing informal reasoning and related Lean 4 code snippets during the reasoning process, the model can better simulate human problem-solving strategies.
- High sample efficiency: With a small number of samples, Kimina-Prover can achieve good results. As computational resources increase, performance improves significantly.
- Model scale is positively correlated with performance: Unlike previous neural theorem provers, Kimina-Prover's performance improves significantly as model size increases.
Technical principles of Kimina-Prover
- Autoformalization: To build a diverse problem set, the researchers trained a model to automatically translate natural language problem statements into Lean 4 code, ending with a placeholder proof.
- Reinforcement learning training: After the supervised fine-tuning (SFT) stage, the model further enhances its formal theorem proving ability 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.
Performance of Kimina-Prover
- Benchmark results: On the miniF2F benchmark, Kimina-Prover achieved 80.7%, exceeding the previous best (SOTA) model by 10.6% and setting a new high.
- Comparison with general-purpose large models: On the miniF2F benchmark and its subsets (such as IMO and AIME), Kimina-Prover significantly outperforms general reasoning models such as OpenAI's o3 and Gemini 2.5 Pro.
Project addresses of Kimina-Prover
- 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
- Scientific research assistance: Kimina-Prover has huge 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 testing: During software development, Kimina-Prover can be used to verify the logical correctness of software. By converting the software's algorithms and logic into the form of mathematical theorems, the model can verify the correctness of these theorems and ensure the reliability and stability of the software.
- Algorithm Verification: In the fields of artificial intelligence and machine learning, Kimina-Prover can be used to verify the correctness and reliability of algorithms, ensuring they are theoretically correct.
- Risk Assessment: In the financial field, Kimina-Prover can be used to verify the mathematical foundations of risk assessment models, ensuring the accuracy and reliability of these models.
- Engineering Design Verification: In engineering design, Kimina-Prover can be used to verify the mathematical models and formulas of designs. In fields such as building structural design and mechanical design, the model can verify the stability and safety of designs.