# LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning

arXiv: https://arxiv.org/abs/2603.21065 · HTML: https://mlsanity.com/paper/2603.21065/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 46 of its 60 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)
- Mixture-of-experts / [MoE in reinforcement learning and robotics](https://mlsanity.com/moe/moe-in-reinforcement-learning-and-robotics/)

## Builds on (most cited first, 30 of 46)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Mastering Complex Control in MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/1912.09729/) (2019)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification](https://mlsanity.com/paper/2503.06639/) (2025)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Towards Robust Mathematical Reasoning](https://mlsanity.com/paper/2511.01846/) (2025)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [Scaling Laws for Native Multimodal Models](https://mlsanity.com/paper/2504.07951/) (2025)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)

## Built on by (most cited first, 7 of 7)

- [Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement](https://mlsanity.com/paper/2606.06468/) (2026)
- [OProver: A Unified Framework for Agentic Formal Theorem Proving](https://mlsanity.com/paper/2605.17283/) (2026)
- [OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond](https://mlsanity.com/paper/2605.19660/) (2026)
- [ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System](https://mlsanity.com/paper/2607.14178/) (2026)
- [AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language](https://mlsanity.com/paper/2607.16372/) (2026)
- [Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification](https://mlsanity.com/paper/2609.11319/) (2026)
- [Humanize Olympiad Agents: A Multi-Session Workflow for Olympiad Problem Solving with Solve, Review, Wiki, Verify](https://mlsanity.com/paper/2610.13632/) (2026)

## Abstract (arXiv)

We introduce LongCat-Flash-Prover, a flagship 560-billion-parameter open-source Mixture-of- Experts (MoE) model that advances Native Formal Reasoning in Lean4 through agentic tool-integrated reasoning (TIR). We decompose the native formal reasoning task into three independent formal capabilities, i.e., auto-formalization, sketching, and proving. To facilitate these capabilities, we propose a Hybrid-Experts Iteration Framework to expand high-quality task trajectories, including generating a formal statement based on a given informal problem, producing a whole-proof directly from the statement, or a lemma-style sketch. During agentic RL, we present a Hierarchical Importance Sampling Policy Optimization (HisPO) algorithm, which aims to stabilize the MoE model training on such long-horizon tasks. It employs a gradient masking strategy that accounts for the policy staleness and the inherent train-inference engine discrepancies at both sequence and token levels. Additionally, we also incorporate theorem consistency and legality detection mechanisms to eliminate reward hacking issues. Extensive evaluations show that our LongCat-Flash-Prover sets a new state-of-the-art for open-weights models in both auto-formalization and theorem proving. Demonstrating remarkable sample efficiency, it achieves a 97.1% pass rate on MiniF2F-Test using only 72 inference budget per problem. On more challenging benchmarks, it solves 70.8% of ProverBench and 41.5% of PutnamBench with no more than 220 attempts per problem, significantly outperforming existing open-weights baselines.