StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion
On the map: LLM reasoning → Mathematical reasoning
Abstract (arXiv)
Autoformalization aims to translate natural-language mathematical statements into a formal language. While LLMs have accelerated progress in this area, existing methods still suffer from low accuracy. We identify two key abilities for effective autoformalization: comprehensive mastery of formal-language domain knowledge, and reasoning capability of natural language problem understanding and informal-formal alignment. Without the former, a model cannot identify the correct formal objects; without the latter, it struggles to interpret real-world contexts and map them precisely into formal expressions. To address these gaps, we introduce ThinkingF, a data synthesis and training pipeline that improves both abilities. First, we construct two datasets: one by distilling and selecting large-scale examples rich in formal knowledge, and another by generating informal-to-formal reasoning trajectories guided by expert-designed templates. We then apply SFT and RLVR with these datasets to further fuse and refine the two abilities. The resulting 7B and 32B models exhibit both comprehensive formal knowledge and strong informal-to-formal reasoning. Notably, StepFun-Formalizer-32B achieves SOTA BEq@1 scores of 40.5% on FormalMATH-Lite and 26.7% on ProverBench, surpassing all prior general-purpose and specialized models.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 42 of its 57 references that are in the map. First posted on arXiv 6 Aug 2025.
Builds on
42 of 57 references.
Closest ancestors · 11
Same direction, newest first
- 2025FMC: Formalization of Natural Language Mathematical Competition Problems15 Jul
- 2025Leanabell-Prover-V2: Verifier-integrated Reasoning for Formal Theorem Proving via Reinforcement Learning11 Jul
- 2025CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics6 May
- 2025FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models5 May
- 2025DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition30 Apr
- 2025Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning15 Apr
- 2025Leanabell-Prover: Posttraining Scaling in Formal Reasoning8 Apr
- 2024Herald: A Natural Language Annotated Lean 4 Dataset9 Oct
- 2024Don't Trust: Verify -- Grounding LLM Quantitative Reasoning with Autoformalization26 Mar
- 2024InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning9 Feb
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models5 Feb
Other references · 31
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2025Qwen3 Technical Reportcited by 8,195
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
- 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
- 2024GPT-4o System Cardcited by 4,467
- 2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,655
- 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,678
- 2023Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generationcited by 1,332
- 2024OpenAI o1 System Cardcited by 1,220
- 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,193
- 2021MiniF2F: a cross-system benchmark for formal Olympiad-level mathematicscited by 380
- 2022Autoformalization with Large Language Modelscited by 252
19 more
- 2023ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematicscited by 180
- 2024PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competitioncited by 153
- 2025Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correctioncited by 140
- 2025Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Provingcited by 126
- 2024Lean Workbook: A large-scale Lean problem set formalized from natural language math problemscited by 115
- 2025Fin-R1: A Large Language Model for Financial Reasoning through Reinforcement Learningcited by 82
- 2024A Survey on Deep Learning for Theorem Provingcited by 55
- 2023Multilingual Mathematical Autoformalizationcited by 38
- 2025QiMeng-CodeV-R1: Reasoning-Enhanced Verilog Generationcited by 34
- 2025CLEVER: A Curated Benchmark for Formally Verified Code Generationcited by 27
- 2025Table-R1: Inference-Time Scaling for Table Reasoningcited by 23
- 2024FVEL: Interactive Formal Verification Environment with Large Language Models via Theorem Provingcited by 22
- 2025Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitionscited by 20
- 2024Divide-and-Conquer Meets Consensus: Unleashing the Power of Functions in Code Generationcited by 19
- 2025Autoformalization in the Era of Large Language Models: A Surveycited by 19
- 2025Kimina Lean Server: A High-Performance Lean Server for Large-Scale Verificationcited by 16
- 2025R1-Code-Interpreter: LLMs Reason with Code via Supervised and Multi-stage Reinforcement Learningcited by 15
- 2025Mathesis: Towards Formal Theorem Proving from Natural Languagescited by 14
- 2025A Short Survey on Formalising Software Requirements using Large Language Modelscited by 4
Built on by
Citing papers per year: 2025: 7; 2026: 8.
15 papers.
Sort:
By area:
- 2025Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graphcited by 18
- 2025ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalizationcited by 18
- 2025ProofBridge: Auto-Formalization of Natural Language Proofs in Lean via Joint Embeddingscited by 16
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similaritycited by 8
- 2025DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theoremscited by 8
- 2025Autoformalizer with Tool Feedbackcited by 7
- 2026LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learningcited by 6
- 2026Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalizationcited by 4
- 2026MathAtlas: A Benchmark for Autoformalization in the Wildcited by 2
- 2026Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Treescited by 1
- 2026FaithformBench: Benchmarking Faithfulness of Mathematical Chain-of-Thought Autoformalisationcited by 1
- 2025TopoAlign: A Framework for Aligning Code to Math via Topological Decompositioncited by 0
3 more
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalizationcited by 0
- 2026Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hintscited by 0
- 2026MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinementcited by 0
- 2026MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement14 Aug 2026
- 2026FaithformBench: Benchmarking Faithfulness of Mathematical Chain-of-Thought Autoformalisation11 Aug 2026
- 2026Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization30 Jun 2026
- 2026MathAtlas: A Benchmark for Autoformalization in the Wild13 May 2026
- 2026Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Trees21 Apr 2026
- 2026Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hints17 Apr 2026
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalization15 Apr 2026
- 2026LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning22 Mar 2026
- 2025ProofBridge: Auto-Formalization of Natural Language Proofs in Lean via Joint Embeddings17 Oct 2025
- 2025ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalization13 Oct 2025
- 2025TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition13 Oct 2025
- 2025DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theorems12 Oct 2025
3 more
- 2025Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graphcited by 18
- 2026LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learningcited by 6
- 2026Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hintscited by 0
- 2026Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hints17 Apr 2026
- 2026LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning22 Mar 2026
- 2025Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph6 Oct 2025
- 2025ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalizationcited by 18
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similaritycited by 8
- 2025DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theoremscited by 8
- 2025Autoformalizer with Tool Feedbackcited by 7
- 2026Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalizationcited by 4
- 2026MathAtlas: A Benchmark for Autoformalization in the Wildcited by 2
- 2026Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Treescited by 1
- 2025TopoAlign: A Framework for Aligning Code to Math via Topological Decompositioncited by 0
- 2026MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinementcited by 0
- 2026MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement14 Aug 2026
- 2026Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization30 Jun 2026
- 2026MathAtlas: A Benchmark for Autoformalization in the Wild13 May 2026
- 2026Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Trees21 Apr 2026
- 2025ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalization13 Oct 2025
- 2025TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition13 Oct 2025
- 2025DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theorems12 Oct 2025
- 2025Autoformalizer with Tool Feedback8 Oct 2025
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity26 Sep 2025
Similar, not cited
Close in wording, no citation either way
- 2025Beyond Gold Standards: Epistemic Ensemble of LLM Judges for Formal Mathematical Reasoning
- 2025ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization
- 2024Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency
- 2025Conjecturing: An Overlooked Step in Formal Mathematical Reasoning
- 2025KELPS: A Framework for Verified Multi-Language Autoformalization via Semantic-Syntactic Alignment
- 2025From Informal to Formal -- Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs
- 2025MASA: LLM-Driven Multi-Agent Systems for Autoformalization
- 2025Thinking Machines: Mathematical Reasoning in the Age of LLMs