First Experiments with Neural Translation of Informal to Formal Mathematics
This addresses the challenge of automating mathematical formalization for mathematicians and formal verification researchers, representing a novel application rather than an incremental improvement.
The authors tackled the problem of automatically translating informal mathematics written in LaTeX into the formal Mizar language using neural networks, achieving 65.73% correct translations with their best model and 79.17% coverage across all models.
We report on our experiments to train deep neural networks that automatically translate informalized LaTeX-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.