FormalAlign: Automated Alignment Evaluation for Autoformalization

Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements remains challenging. Existing approaches heavily rely on manual verification, hindering scalability. To address this, we introduce textscFormalAlign, the first automated framework designed for evaluating the alignment between natural and formal languages in autoformalization. textscFormalAlign trains on both the autoformalization sequence generation task and the representational alignment between input and output, employing a dual loss that combines a pair of mutually enhancing autoformalization and alignment tasks. Evaluated across four benchmarks augmented by our proposed misalignment strategies, textscFormalAlign demonstrates superior performance. In our experiments, textscFormalAlign outperforms GPT-4, achieving an Alignment-Selection Score 11.58% higher on forml-Basic (99.21% vs. 88.91%) and 3.19% higher on MiniF2F-Valid (66.39% vs. 64.34%). This effective alignment evaluation significantly reduces the need for manual verification. Both the dataset and code can be accessed via~urlhttps://github.com/rookie-joe/FormalAlign.