DeepSeek-Prover advances theorem proving through reinforcement learning and Monte-Carlo Tree Search with proof assistant feedbac

The research paper on DeepSeek-Prover-V1.5 presents a system that enhances automated theorem proving by integrating reinforcement learning and Monte-Carlo Tree Search (MCTS), with feedback from proof assistants. The system learns to navigate complex search spaces for logical steps in mathematical proofs, where reinforcement learning guides the system based on feedback from proof assistants about the validity of the steps. MCTS aids in exploring potential solutions by simulating many possible sequences and identifying the most promising paths. DeepSeek-Prover-V1.5's technical design includes these components working in synergy, significantly improving its performance on challenging mathematical problems compared to traditional approaches. However, the paper acknowledges certain limitations, such as the system's heavy dependence on the proof assistant's capabilities, which could limit learning effectiveness if the assistant has biases or restrictions. Another concern is scalability, as the system has primarily been tested on smaller problems, leaving its effectiveness on larger, more complex proofs uncertain. The system's interpretability is also questioned, as understanding its decision-making process might be challenging, which is crucial for building trust and further refinement. The paper suggests that further research is necessary, particularly in testing the system's ability to generalize its knowledge to new, unseen problems and exploring its performance on more significant issues. Despite these limitations, the paper recognizes DeepSeek-Prover-V1.5 as a significant advancement in automated theorem proving, with potential applications in various fields like mathematics and computer science. If the system's limitations are addressed, it could become a powerful tool for researchers, helping them solve complex problems more efficiently.