This article discusses the concept of autoformalization, which involves converting informal mathematical knowledge into verifiable formalizations. The researchers used a large language model, GPT-4, to create a parallel dataset called MMA, containing informal-formal pairings in multiple formal languages. They trained the language model on MMA and found it to have strong autoformalization capabilities. The MMA dataset and optimized models are made available for further research.
Can Autoformalization Bridge the Gap Between Informal and Formal Language? Meet MMA: A Multilingual and Multi-Domain Dataset Revolutionizing the Field
Autoformalization, the process of converting informal mathematics into formally provable material, has been a long-standing challenge in the field of mathematics. However, recent advances in neural networks and Neural Machine Translation have made it possible to teach autoformalization using cutting-edge technologies.
Researchers from the University of Cambridge and the University of Edinburgh have developed a groundbreaking solution called MMA (Multilingual and Multi-Domain Dataset) to address the lack of parallel datasets for autoformalization research. By using a Large Language Model called GPT-4, they were able to convert the two largest formal corpora, Archive of Formal Proofs in Isabelle and mathlib4 in Lean4, into natural language.
The MMA dataset, which contains informal-formal pairings, is the first parallel dataset with multiple formal languages and is four times larger than any existing dataset. The researchers optimized an open-source LLM called LLaMA-33B on MMA to provide formal phrases corresponding to informal ones. The trained model was then evaluated on two autoformalization benchmarks, miniF2F and ProofNet, and achieved a significant improvement in producing formal statements.
Contributions:
- Creation of MMA, a collection of informal-formal pairings from mathlib4 and the Archive of Formal Proofs.
- Training of the first language model capable of autoformalization in multiple languages, with evaluation on autoformalization benchmarks.
- Confirmation of the robust autoformalization capabilities of language models trained on MMA.
- Availability of optimized models and the MMA dataset for deduction and further training.
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