ATLAS: Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data

Autoformalization, the process of automatically translating natural language mathematics into machine-verifiable formal language, has demonstrated advancements with the progress of large language models (LLMs). However, a key obstacle to further advancements is the scarcity of paired datasets that align natural language with formal language. To address this challenge, we introduce ATLAS (Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data), an iterative data generation framework designed to produce large-scale, high-quality parallel theorem statements. With the proposed ATLAS running for 10 iterations, we construct an undergraduate-level dataset comprising 300k theorem statements and develop the ATLAS translator, achieving accuracies of 80.59% (pass@8) and 92.99% (pass@128) on ProofNet, significantly outperforming the base model (23.99% and 47.17%) and InternLM2-Math-Plus-7B (50.94% and 80.32%). Furthermore, the ATLAS translator also achieves state-of-the-art performance on both the high-school-level miniF2F dataset and the graduate-level MathQual dataset introduced in this work. The datasets, model, and code will be released to the public soon.