DeepSeek-Prover-V1.5 - An open-source mathematical model with 7 billion parameters

What is DeepSeek-Prover-V1.5?

DeepSeek-Prover-V1.5 is an open-source mathematical model developed by the DeepSeek team, boasting 7 billion parameters. By combining reinforcement learning (RLPAF) and Monte Carlo tree search (especially the RMaxTS variant), the model achieves significant improvements in efficiency and accuracy in proving mathematical theorems. On high school and university-level mathematical problems, DeepSeek-Prover-V1.5 outperforms all other open-source models on the Lean 4 platform, setting a new state-of-the-art (SOTA) standard. It not only validates existing proofs but also has the potential to help create new mathematical knowledge, propelling mathematical research into the era of "Big Mathematics."

Main features of DeepSeek-Prover-V1.5

• Reinforcement learning optimizationThe model employs reinforcement learning based on proof assistant feedback (RLPAF), using the verification results of the Lean prover as a reward signal to optimize the proof generation process.
• Monte Carlo Tree SearchIntroducing the RMaxTS algorithm, a variant of Monte Carlo tree search, to address the reward sparsity problem in proof search and enhance the model's exploratory behavior.
• Prove generation capabilityThe model can generate proofs of mathematical theorems at the high school and university levels, significantly improving the success rate of proofs.
• Pre-training and fine-tuningPre-training on high-quality mathematical and code data, and supervised fine-tuning on the Lean 4 code completion dataset, improves the model's formal proof capabilities.
• Aligning Natural Language with Formal ProofUsing DeepSeek-Coder V2 to annotate natural language thought chains alongside Lean 4 code, combining natural language reasoning with formal theorem proofs.

Technical Principles of DeepSeek-Prover-V1.5

• Pre-training:DeepSeek-Prover-V1.5 has undergone further pre-training on mathematical and code data, focusing on formal mathematical languages such as Lean, Isabelle, and Metamath to enhance the model's ability in formal theorem proving and mathematical reasoning.
• Supervised fine-tuning:Specific data augmentation techniques, including adding natural language thought chain annotations next to Lean 4 code and inserting intermediate policy state information into the proof code, are used to improve the model’s understanding of the consistency between natural language and formal proof.
• Reinforcement Learning:The GRPO algorithm is used for reinforcement learning based on proof assistant feedback. The verification results of the Lean prover are used as reward signals to further optimize the model and make it more consistent with the requirements of the formal verification system.
• Monte Carlo Tree Search (MCTS):A novel tree search method is introduced, which decomposes incomplete proofs into a sequence of tree nodes through a truncation and restart mechanism, and uses these nodes to continue the proof generation process.
• Intrinsic Rewards for Exploration:Using the RMaxTS algorithm, DeepSeek-Prover-V1.5 uses intrinsic rewards to drive exploration behavior, encouraging the model to generate diverse proof paths and solving the problem of reward sparsity in proof search.

Project address for DeepSeek-Prover-V1.5

• Product Websitedeepseek.com
• GitHub repository:https://github.com/deepseek-ai/DeepSeek-Prover-V1.5
• arXiv technical paper:https://arxiv.org/pdf/2408.08152

How to use DeepSeek-Prover-V1.5

• Environment configuration:Make sure all necessary software and dependencies are installed, such as the Lean proof helper, as well as any other possible programming language environments.
• Get the model:Access DeepSeek-Prover-V1.5GitHub repositoryClone or download the model's codebase to your local machine.
• Model installation:Installing the model according to the provided installation guide may include compiling the code, installing Python libraries, or other dependencies.
• Data preparation:The descriptions of mathematical problems and theorems that need to be prepared or generated need to be written in a specific format so that the model can understand them.
• Interactive interface:Interact with the model using the command-line interface or graphical user interface (if provided), and enter mathematical problems or theorems.
• Proof generation:Run the model and let it process the input mathematical problem. The model will attempt to generate a proof or provide proof steps.

Application Scenarios of DeepSeek-Prover-V1.5

• Mathematical research:It assists mathematicians and researchers in quickly verifying and generating complex mathematical proofs when exploring new mathematical theories and proofs.
• Education:In higher education, it helps students learn and understand the proof process of mathematical theorems and improve their mathematical reasoning ability.As a teaching tool, it automatically generates proof steps for practice questions, providing students with a learning reference.
• Automated theorem proving:In the field of formal verification, DeepSeek-Prover-V1.5 can be used to automatically prove the correctness of mathematical software and systems.
• Software development:It can be integrated into the software development process to help developers understand and verify the mathematical foundations of algorithms.