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Autoformalization in the Era of Large Language Models: A Survey
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Autoformalization in the Era of Large Language Models: A Survey
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Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both theoretical and applied domains. Driven by the rapid progress in artificial intelligence, particularly large language models (LLMs), this field has witnessed substantial growth, bringing both new opportunities and unique challenges. In this survey, we provide a comprehensive overview of recent advances in autoformalization from both mathematical and LLM-centric perspectives. We examine how autoformalization is applied across various mathematical domains and levels of difficulty, and analyze the end-to-end workflow from data preprocessing to model design and evaluation. We further explore the emerging role of autoformalization in enhancing the verifiability of LLM-generated outputs, highlighting its potential to improve both the trustworthiness and reasoning capabilities of LLMs. Finally, we summarize key open-source models and datasets supporting current research, and discuss open challenges and promising future directions for the field.
Forward citations
Cited by 10 Pith papers
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FormalRx: Rectify and eXamine Semantic Failures in Autoformalization
FormalRx diagnoses Lean autoformalization failures with a 28-category SCI taxonomy and an 8B model that jointly predicts alignment, error type, location, and correction.
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Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabeling
Audit finds 36-39% incorrect FOL labels in FOLIO and MALLS; corrections raise LLM accuracy 9-22 points and an LLM-guided review framework achieves 90% dataset quality after checking fewer than 24% of examples.
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CAM-Bench: A Benchmark for Computational and Applied Mathematics in Lean
CAM-Bench is a new Lean 4 theorem-proving benchmark of 1,000 problems in computational and applied mathematics, built from textbook exercises using a dependency-recovery pipeline to reconstruct local context.
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From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.
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Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization
A 400-entry benchmark and protocol shows tool-augmented agents reach 89.5% compilation but only 60.5% consensus faithfulness, with a 29-point gap; elaboration feedback improves validity most but increases unfaithful compiles.
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External verification structures, not model capability, determine the reliability of LLM-assisted economic theory, as shown in attempts to design an incentive mechanism for a grade inflation model where adversarial ch...
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Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematics
Visored is a controlled-natural-language prover for LLM math that automates omitted routine steps and emits checked Lean output, with early miniF2F results showing LLMs can use it without prover-specific training.
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SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalization
Disjoint SFT and GRPO data for autoformalization yields up to 10.4pp semantic accuracy gains over full overlap, which renders the GRPO stage redundant.
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Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics
Ax-Prover is a tool-using multi-agent LLM system that matches state-of-the-art provers on public math benchmarks and outperforms them on new abstract-algebra and quantum-theory benchmarks while also assisting an exper...
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Autoformalization of Agent Instructions into Policy-as-Code
An LLM-based generator-critic loop autoformalizes natural language policies into Cedar policies that cover substantially more of the source specification than hand-coded symbolic enforcement on MedAgentBench.
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