# MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement

arXiv: https://arxiv.org/abs/2608.14221 · HTML: https://mlsanity.com/paper/2608.14221/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
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- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics](https://mlsanity.com/paper/2505.03171/) (2025)
- [FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels](https://mlsanity.com/paper/2511.02872/) (2025)
- [LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover](https://mlsanity.com/paper/2407.17227/) (2024)
- [DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning](https://mlsanity.com/paper/2505.23754/) (2025)
- [Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph](https://mlsanity.com/paper/2510.04520/) (2025)
- [ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization](https://mlsanity.com/paper/2510.24592/) (2025)
- [Mathesis: Towards Formal Theorem Proving from Natural Languages](https://mlsanity.com/paper/2506.07047/) (2025)
- [LeanExplore: A search engine for Lean 4 declarations](https://mlsanity.com/paper/2506.11085/) (2025)
- [Kimina Lean Server: A High-Performance Lean Server for Large-Scale Verification](https://mlsanity.com/paper/2504.21230/) (2025)
- [StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion](https://mlsanity.com/paper/2508.04440/) (2025)
- [DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theorems](https://mlsanity.com/paper/2510.10815/) (2025)
- [Autoformalizer with Tool Feedback](https://mlsanity.com/paper/2510.06857/) (2025)
- [Reasoning over mathematical objects: on-policy reward modeling and test time aggregation](https://mlsanity.com/paper/2603.18886/) (2026)
- [MA-ProofBench: A Two-Tiered Evaluation of LLMs for Theorem Proving in Mathematical Analysis](https://mlsanity.com/paper/2606.13782/) (2026)

## Abstract (arXiv)

Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4. However, faithful formalization requires more than translation. Models must map mathematical concepts to the complex hierarchy of types and definitions in formal libraries such as Mathlib, while ensuring that generated statements preserve the meaning of the source propositions. Existing approaches struggle because they rely heavily on the model's parametric memory for library-specific knowledge, while common data construction pipelines often resort to filtering single-pass outputs and lack mechanisms for feedback-driven revision. To address these challenges, we introduce MathForm, an autoformalization framework for constructing verified training data through Mathlib knowledge retrieval and verification-guided iterative refinement. Before generation, a retrieval planner gathers relevant definitions and existing formalizations from Mathlib to guide the formalization generator. Generated statements are then revised using compiler diagnostics and semantic-consistency feedback. Using this framework, we construct FormalVerse, a Lean 4 dataset containing approximately 367K verified examples across diverse mathematical domains and sources. We then train MathForm-8B through supervised fine-tuning followed by reinforcement learning. Across six benchmarks, MathForm-8B achieves average Pass@8 rates of 88.06% under Syntax Check (SC) and 72.37% under Consistency Check (CC), outperforming multiple specialized 32B autoformalizers. On the challenging FATE-H and FATE-X subsets, it attains CC pass rates of 63% and 37%, exceeding the strongest specialized baselines in both cases.