ByteDance Introduces Seed-Prover: An Advanced Formal Reasoning System for Automated Mathematical Theorem Proving

Understanding the Target Audience

The target audience for ByteDance’s Seed-Prover includes academic researchers, mathematicians, AI developers, and business professionals engaged in mathematical modeling or algorithm development. These individuals typically share the following characteristics:

• Pain Points: Difficulty in verifying the correctness of mathematical proofs, challenges in applying reinforcement learning (RL) to theorem proving, and limitations of current formal languages in handling complex proofs.
• Goals: To improve the efficiency and accuracy of mathematical theorem proving, harness AI capabilities for complex problem-solving, and develop robust systems that can handle high-level reasoning.
• Interests: Advances in AI and machine learning techniques, formal methods in mathematics, and innovations in automated reasoning.
• Communication Preferences: Preference for technical, detailed content that includes peer-reviewed statistics, practical applications, and case studies relevant to AI and business management.

Overview of Seed-Prover

ByteDance’s Seed Team has introduced Seed-Prover, a lemma-style whole-proof reasoning model designed to refine mathematical proofs iteratively through Lean feedback, previously established lemmas, and self-summarization. This system employs three specialized test-time inference strategies that enhance reasoning methods to address International Mathematical Olympiad (IMO)-level contest problems. The core innovation lies in adopting lemma-style proving, which centers lemmas in the reasoning process rather than relying on traditional step-by-step or whole-proof generation methods.

Key Features

• Integration with Lean: Seed-Prover uses multi-stage, multi-task RL based on VAPO for interaction with Lean, enabling enhanced proof verification.
• Efficient Problem Generation: Seed-Geometry’s backend can generate over 230 million unique problems within one week, achieving an eightfold improvement in search efficiency.
• Performance Metrics: Seed-Prover has demonstrated state-of-the-art results across multiple mathematical benchmarks, solving 5 out of 6 problems in IMO 2025 and achieving a 78.1% success rate across different problem categories.

Performance Insights

In the context of various mathematical competitions and benchmarks:

• IMO 2025: Seed-Prover solved 5 out of 6 problems, with Seed-Geometry solving Problem 2 instantly.
• Past IMO Problems: Proved 121 out of 155 tasks, with success rates of 47 out of 55 for easy problems, 47 out of 56 for medium problems, and 27 out of 44 for hard problems.
• MiniF2F: Achieved a 99.6% proof rate under medium settings.
• PutnamBench: Improved from 201 to 331 solved problems out of 657 by upgrading inference settings.
• CombiBench: Solved 30 out of 100 combinatorics problems, outperforming existing methods.
• MiniCTX-v2: Achieved an 81.8% success rate, significantly surpassing previous baselines.

Future Directions

ByteDance aims to combine formal systems with large language models (LLMs) to tackle open conjectures and further enhance the capabilities of automated reasoning systems. The integration of formal languages like Lean offers rapid proof verification that is more cost-effective than human experts and more reliable than LLM-based judges.

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