Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience

2025-12-19

AI Summary

To address the high computational cost and limited generalization of large language models (LLMs) in undergraduate- and graduate-level theorem proving within formal systems like Lean, this paper proposes an agent-based reinforcement learning paradigm for experience-driven learning. The method leverages high-quality formal feedback as supervisory signals and introduces a natural-language–formal-language co-guided test-time scaling (TTS) workflow to enable efficient experience accumulation and policy optimization under constrained compute. Key innovations include the first formal-feedback-driven continual experience learning mechanism and a cross-modal alignment-enhanced TTS inference framework. Experiments demonstrate state-of-the-art performance: 88%, 80%, and 33% accuracy on PutnamBench, Fate-H, and Fate-X, respectively; notably, the approach solves 11 of the 12 problems from Putnam 2025 within nine hours.

Technology Category

• Multiagent Systems: Multiagent Learning
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Large language models have recently made significant progress to generate rigorous mathematical proofs. In contrast, utilizing LLMs for theorem proving in formal languages (such as Lean) remains challenging and computationally expensive, particularly when addressing problems at the undergraduate level and beyond. In this work, we present extbf{Seed-Prover 1.5}, a formal theorem-proving model trained via large-scale agentic reinforcement learning, alongside an efficient test-time scaling (TTS) workflow. Through extensive interactions with Lean and other tools, the model continuously accumulates experience during the RL process, substantially enhancing the capability and efficiency of formal theorem proving. Furthermore, leveraging recent advancements in natural language proving, our TTS workflow efficiently bridges the gap between natural and formal languages. Compared to state-of-the-art methods, Seed-Prover 1.5 achieves superior performance with a smaller compute budget. It solves extbf{88% of PutnamBench} (undergraduate-level), extbf{80% of Fate-H} (graduate-level), and extbf{33% of Fate-X} (PhD-level) problems. Notably, using our system, we solved extbf{11 out of 12 problems} from Putnam 2025 within 9 hours. Our findings suggest that scaling learning from experience, driven by high-quality formal feedback, holds immense potential for the future of formal mathematical reasoning.

Problem

• Enhances formal theorem proving efficiency with agentic reinforcement learning
• Bridges natural and formal language gaps via test-time scaling workflow
• Solves undergraduate to PhD-level problems with reduced computational cost

Innovation

• Large-scale agentic reinforcement learning for formal theorem proving
• Efficient test-time scaling workflow bridging natural and formal languages
• Continuous experience accumulation through interaction with Lean tools