Autoformalization

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Overview

Autoformalization translates informal mathematical statements, proofs, and software or scientific requirements into forms that proof assistants and solvers can check. Systems commonly combine language models with library retrieval, dependency-aware decomposition, and iterative feedback from Lean or Isabelle checkers, provers, model checkers, and tests. Benchmarks span competition and textbook mathematics, first-order logic, and executable software specifications, while agentic workflows increasingly tackle larger theories and research developments. The central challenge is semantic faithfulness: a formal artifact can compile or verify while misstating its source, so evaluation increasingly combines execution with equivalence checks, adversarial tests, and human review.

Latest papers

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115 papers17 papers in the last four weeks, up 89% on the four weeks before. 0.1% of all new papers.

  1. MechAlign: Evaluating Semantic Alignment at the Project Level in Mathematical Formalization

    Oct 26, 2026Hao Shen, Ruichen Qiu, Lihong Zhi +1Semantic AlignmentAutomated Evaluation

    State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences.

  2. SemantEq: Faithful Bidirectional Equivalence of Formal Statements

    Oct 23, 2026Xinrui Li, Pawan Sasanka Ammanamanchi, Siddharth Bhat +3Formal VerificationLean Theorem Proving

    EleutherAI · Carnegie Mellon University · University of Cambridge +1

  3. PaperFormalizer: Author-in-the-Loop Autoformalization of Research Papers in Lean

    Oct 22, 2026Jiyuan Tan, Vasilis Syrgkanis, Jose BlanchetAutoformalizationFormal Verification

    Stanford University

  4. ALIAS: Evaluating Performance and Memorization in LLM-Written TLA+ Specifications

    Oct 21, 2026Arslan Bisharat, Mujtaba Nazari, Khushboo Bhadauria +7Memorization in Language ModelsLanguage Model Reasoning Evaluation

    Loyola University Chicago

  5. Repairing LLM-Generated Specifications with Deterministic Diagnosis

    Oct 15, 2026Giovanni Vaccarino, Emanuele La Malfa, Dehai Min +6AutoformalizationLLM Self-Correction

    Department of Computer Science, University of Oxford, Oxford, UK · Department of Computer Science, University of Illinois Chicago, Chicago, IL, USA · Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy +2

  6. Beyond LLM Judge: Mechanical Verification for Agentic Autoformalization

    Oct 14, 2026Anna Mei, Michael R. DouglasFormal VerificationAutoformalization

    Harvard University · CMSA, Harvard University and AletheAI, Inc

  7. Definition Grounding in Theory-Level Auto-formalization

    Oct 13, 2026Leyan Pan, Christian Szegedy, Frederick Rajasekaran +3AutoformalizationLean Theorem Proving

    Georgia Institute of Technology · AletheAI · Stanford University

  8. Aligning Faithfulness for Theory-Scale Autoformalization

    Oct 13, 2026Yuming Feng, Tadd Mao, Dhruva Arekar +4Contextual FaithfulnessAutoformalization

    Johns Hopkins University · University of Toronto · University of Pennsylvania

  9. A dataset of formalised theorem statements from the Annals of Mathematics

    Oct 13, 2026Thomas Browning, Katerina Hristova, David Ledvinka +4AutoformalizationMathematical Reasoning Benchmarks

    Department of Mathematics, Imperial College London · Department of Philosophy, Carnegie Mellon University

  10. claimcheck: Measuring and Improving Specification Faithfulness

    Oct 12, 2026Martin Amster, One An, Holly Baker +3AutoformalizationFormal Verification

    Universidad de Buenos Aires Buenos Aires, Argentina · University of Pennsylvania Philadelphia, PA 19104, USA · PolicingLab Dublin, Ireland +3

  11. Natural Language to First-Order Logic LLM-based Autoformalization

    Oct 8, 2026Andrea Brunello, Cristian Curaba, Luca Geatti +3Autoformalization

    University of Udine, Italy

  12. Beyond Type-checking: Towards Holistic Evaluation of Formal Specification Generation

    Oct 7, 2026Srijith Nair, Aditya Vempaty, Jia Liu +1Formal VerificationAutoformalization

    Department of Electrical & Computer Engineering The Ohio State University · Emergence AI

  13. An AI-Assisted Formalization of the Poincaré Conjecture

    Oct 6, 2026Zhiyuan Zhang, Axel Delaval, Leheng Chen +6Human-AI CollaborationHuman-in-the-Loop AI

    School of Mathematical Sciences, Peking University · Beijing International Center for Mathematical Research, Peking University · Zhongguancun Academy +5

  14. Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs

    Oct 6, 2026Alexander Bastounis, Fabian Circelli, Anders C. HansenAutoformalizationFormal Verification

  15. AIProver: Agentic Auto-Formalization of Mathematical Research via Certificate-Driven Evolving Harness

    Oct 4, 2026Prithwish Jana, Viet Bach Hoang, Logan Luna +9Mathematical Reasoning BenchmarksAutomated Theorem Proving

    Georgia Institute of Technology, USA · University of Pennsylvania, USA · Foothill College, USA +3

  16. Law And Order: Tax Law Autoformalization

    Oct 2, 2026Sophia Simeng Han, Yoshiki Takashima, Anjiang Wei +2AutoformalizationProgram Synthesis

    Stanford University · Stanford Law School · Pramaana Labs +1

  17. Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization

    Sep 30, 2026Wei Zhao, Yangshuo Zou, Chengxiang Ding +5Automated Theorem ProvingHuman-in-the-Loop AI

    School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China · University of California, Berkeley, CA 94720, USA · Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China +4

  18. ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization

    Sep 28, 2026Feiming Wang, Daibo Li, Kun YuanStochastic OptimizationLarge Language Model-Guided Theorem Proving

    Nankai University · Peking University

  19. Choir: An Open Protocol for Distributed Multi-Agent Autoformalization

    Sep 25, 2026Yidi Qi, Melanie WeberMulti-Agent CollaborationLLM Agent Orchestration

    Harvard University

  20. Lean Pool: An AI-Maintained Archive of Formalized Mathematics

    Sep 21, 2026Vasily IlinAI Coding AgentsInteractive Theorem Proving

    University of Washington

  21. Long-horizon autoformalization of a core theorem underlying MIP* = RE

    Sep 17, 2026Sirui Lu, Ruixuan Deng, Yanqiao Zhu +1Automated Theorem ProvingFormal Verification

    Max‑Planck‑Institut für Quantenoptik, Hans‑Kopfermann‑Straße 1, D‑85748 Garching, Germany · Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D‑80799 Munich, Germany · Department of Computer Science and Technology, Tsinghua University +1

  22. MAGS: Multi-agent Auto-formalization Guarantees Safety for Agentic Outputs

    Sep 16, 2026Albert Wu, Nicholas Roberts, Tzu-Heng Huang +5Multi-Agent LLM SystemsFormal Verification

    University of Wisconsin-Madison · Princeton University

  23. Sage: Formalization with Semantic Correction

    Sep 16, 2026Thomas Hirtz, Farzad Jafarrahmani, Abdelmouksit Sagueni +3LLM Self-CorrectionLean Theorem Proving

    Huawei Lagrange Mathematics and Computing Research Center Paris, France

  24. Autoformalizing Argumentative Material Inferences

    Sep 15, 2026Xin Quan, Reto Gubelmann, André FreitasLogical ReasoningInteractive Theorem Proving

    1Idiap Research Institute, Switzerland · University of Zurich, Switzerland · Department of Computer Science, University of Manchester, UK

  25. Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification

    Sep 10, 2026Joshua Ong Jun Leang, Haonan Li, Zheng Zhao +6Automated Theorem ProvingAgentic Reasoning

    Institute of Foundation Models · Imperial College London · University of Edinburgh +1

  26. Beyond Solver Verdicts: Generative Reward Models for Autoformalization

    Sep 10, 2026Vikash Singh, Debargha Ganguly, Aman Goel +5Reward ModelingFormal Verification

    Case Western Reserve University · Amazon Web Services

  27. AxQM: A Textbook-Scale Benchmark for Formal Proof Synthesis in a Library of Finite-Dimensional Quantum Mechanics

    Sep 4, 2026Weichen Winston Yin, Jacob M. Taylor, Dirk R. Englund +1AutoformalizationAutomated Theorem Proving

    Axiomatic AI. · Massachusetts Institute of Technology (MIT) · Institut de Ciències Fotòniques (ICFO). +1

  28. SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization

    Aug 29, 2026Hojae Han, Jongyoon Kim, Sanghyeok Park +8Autoformalization

    Electronics and Telecommunications Research Institute · Seoul National University · Sejong University +1

  29. NL2AGBench: Benchmarking LLM Auto-Formalization for AlphaGeometry

    Aug 28, 2026Samuel Xiao, Judy Song, Rory Hu +1AutoformalizationLLM Evaluation

    Valley Christian High School Fremont, CA · Vandegrift High School Austin, TX · Groton School Cupertino, CA +1

  30. MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

    Aug 26, 2026Jiaxin Yuan, Udari Madhushani Sehwag, Connor Martinez Lockhart +13Mathematical Reasoning BenchmarksAutomated Theorem Proving

    University of Maryland, College Park · Georgia Institute of Technology · Cornell University +2