LongCat-Flash-Prover - Meituan's Open-Source Mathematical Theorem Proving Model

What is LongCat-Flash-Prover

LongCat-Flash-Prover is a 560-billion-parameter MoE model open-sourced by Meituan, focused on Lean4 formal mathematical reasoning. Through Agentic Tool-Integrated Reasoning (TIR), the model decomposes tasks into three major capabilities: autoformalization, sketch generation, and theorem proving. LongCat-Flash-Prover adopts a mixture-of-experts iterative framework and the HisPO reinforcement learning algorithm for stable training, and introduces anti-cheating mechanisms to ensure reasoning rigor. It achieves SOTA levels on benchmarks such as MiniF2F-Test, with 93.9% Pass@32 accuracy and a 28.9% solve rate on hard PutnamBench problems, significantly surpassing existing open-source models.

LongCat-Flash-Prover's Main Features

• Autoformalization: Supports converting natural language mathematical problems into verified Lean4 formal statements.
• Sketch Generation: Generates lemma-style proof frameworks based on the problem and formal statement.
• Theorem Proving: Supports generating complete proofs or introducing auxiliary lemmas to complete the proof of the target theorem.
• Tool-Integrated Reasoning: The model can directly invoke the Lean4 compiler for real-time verification and feedback iteration.

LongCat-Flash-Prover's Technical Principles

• Mixture-of-Experts Iterative Framework: The framework supports deploying multiple specially optimized expert models, each responsible for different domain tasks such as autoformalization, sketch generation, and proving. By having expert models generate reasoning trajectories with tool assistance and perform iterative optimization, it simulates the human learning process of trial and error, verification, and reflection, expanding high-quality cold-start data.
• Hierarchical Importance Sampling Policy Optimization (HisPO): Addressing the instability of MoE models in long-horizon task training, HisPO adopts a hierarchical clipping strategy that estimates importance sampling ratios at both the sequence level and the token level, eliminating gradient contributions with large discrepancies between the training and inference engines, thereby stabilizing the reinforcement learning training process.
• Anti-Reward-Hacking Mechanism: The system introduces theorem consistency detection and validity detection to identify and filter out proofs that are semantically inconsistent with the formal statement, have mismatched conditions, or contain unverified axioms, preventing the model from obtaining false rewards by deceiving the Lean4 server.

LongCat-Flash-Prover's Key Information and Usage Requirements

• Model Scale: Adopts a 560-billion-parameter MoE architecture, one of the largest parameter counts among open-source weight models
• Core Positioning: Focused on Lean4 native formal reasoning, requiring no modification of the model architecture for formalization tasks
• Performance Breakthroughs: MiniF2F-Test reaches 93.9% (Pass@32), PutnamBench reaches 28.9%, both SOTA among open-source models
• Inference Efficiency: On MiniF2F-Test, only 72 inference runs are needed to reach a 97.1% pass rate, with extremely high sample efficiency
• Training Data: Synthesizes high-quality trajectories through the mixture-of-experts iterative framework, supporting three task types: autoformalization, sketching, and proving
• Hardware Environment: The 560B-parameter MoE model requires large-scale GPU cluster support for inference; a multi-GPU environment with ample VRAM is recommended
• Software Dependencies: Requires installation of the Lean4 proof assistant and the corresponding toolchain; the model performs real-time verification interaction through the Lean4 server
• Deployment Method: Supports Whole-Proof mode (directly generating a complete proof) and Sketch-Proof mode (first sketching, then completing); the latter works better with TIR

Core advantages of LongCat-Flash-Prover

• Native capability: Treats formal reasoning as a native LLM capability, requiring no specialized architectural modifications and able to directly invoke the Lean4 toolchain, achieving deep integration with the formal environment.
• SOTA performance: Leads open-source models across all five major benchmarks—MathOlympiad-Bench, MiniF2F-Test, ProofNet, ProverBench, and PutnamBench—with some metrics approaching or surpassing closed-source commercial models.
• Sample efficient: Requires only 72 inference runs to reach a 97.1% pass rate on MiniF2F-Test, far fewer attempts than comparable models, significantly reducing inference cost.
• Anti-cheating design: Through theorem consistency detection and validity detection mechanisms, ensures the model's outputs are authentic and trustworthy, avoiding false proofs caused by reward hacking.

How to use LongCat-Flash-Prover

• Environment preparation: Install the Lean4 proof assistant and its dependency toolchain, and configure the GPU environment required for model inference, ensuring sufficient VRAM to support loading and running the 560B-parameter MoE model.
• Obtain the model: Download the model weights from the HuggingFace repository, or directly use the inference interface and example code provided on GitHub for deployment.
• Choose the inference mode: According to task complexity, choose Whole-Proof mode to directly generate a complete proof, or choose Sketch-Proof mode to first output a lemma framework and then fill it in step by step.
• Input the problem: Input a natural language mathematical problem or a theorem to be proved into the model; the model automatically invokes the Lean4 compiler for real-time verification and iteratively optimizes the proof process based on feedback.
• Obtain the result: The model outputs a formal proof that has passed Lean4 verification, which can be directly used in mathematical formal verification, theorem library construction, or academic research.

Project address of LongCat-Flash-Prover

• GitHub repository：https://github.com/meituan-longcat/LongCat-Flash-Prover
• HuggingFace model library：https://huggingface.co/meituan-longcat/LongCat-Flash-Prover
• Technical paper：https://github.com/meituan-longcat/LongCat-Flash-Prover/blob/main/LongCat_Flash_Prover_Technical_Report.pdf

Comparison of LongCat-Flash-Prover with similar competing products

Application scenarios of LongCat-Flash-Prover

• Academic mathematical research: Assists mathematicians in transforming natural language conjectures into Lean4 formal statements and automatically verifying them, accelerating the process of proof discovery, and is especially suitable for fields requiring rigorous logical derivation such as algebraic geometry and number theory.
• Mathematical competition training: Provides solution idea verification and formal proof generation for high-level mathematical competitions such as IMO and Putnam, helping contestants understand the rigorous proof structure of complex problems.
• Formal verification engineering: In scenarios such as software correctness proofs, cryptographic protocol verification, and hardware design verification, automatically generates or assists in constructing formal proofs, improving the security of critical systems.
• Educational assistance tool: As an intelligent mathematics teaching assistant, provides students with step-by-step guidance from problem understanding to complete proof, detects reasoning gaps in real time, and gives correction suggestions.