First Experiments with Neural Translation of Informal to Formal Mathematics

• Published in: Intelligent Computer Mathematics Vol. 11006; pp. 255 - 270
• Main Authors: Wang, Qingxiang, Kaliszyk, Cezary, Urban, Josef
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 01.01.2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: BLEU Rate; Long Short-term Memory (LSTM); Neural Machine Translation (NMT); Seq2seq Model; Target Sentence
• ISBN: 3319968114; 9783319968117
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-96812-4_22

We report on our experiments to train deep neural networks that automatically translate informalized -written Mizar texts into the formal Mizar language. To the best of our knowledge, this is the first time when neural networks have been adopted in the formalization of mathematics. Using Luong et al.’s neural machine translation model (NMT), we tested our aligned informal-formal corpora against various hyperparameters and evaluated their results. Our experiments show that our best performing model configurations are able to generate correct Mizar statements on 65.73% of the inference data, with the union of all models covering 79.17%. These results indicate that formalization through artificial neural network is a promising approach for automated formalization of mathematics. We present several case studies to illustrate our results.