Abstract
We have implemented a machine translation system, the PolyMath Translator, for LaTeX documents containing mathematical text. The current implementation translates English LaTeX to French LaTeX, attaining a BLEU score of 53.6 on a held-out test corpus of mathematical sentences. It produces LaTeX documents that can be compiled to PDF without further editing. The system first converts the body of an input LaTeX document into English sentences containing math tokens, using the pandoc universal document converter to parse LaTeX input. We have trained a Transformer-based translator model, using OpenNMT, on a combined corpus containing a small proportion of domain-specific sentences. Our full system uses this Transformer model and also Google Translate with a custom glossary, the latter being used as a backup to better handle linguistic features that do not appear in our training dataset. Google Translate is used when the Transformer model does not have confidence in its translation, as determined by a high perplexity score. Ablation testing demonstrates that the tokenization of symbolic expressions is essential to the high quality of translations produced by our system. We have published our test corpus of mathematical text. The PolyMath Translator is available as a web service at http://www.polymathtrans.ai.
Highlights
Machine translation for specialized domains such as legal or medical text has received considerable attention
We examine how mathematical text differs from text in other domains, and provide evidence that mathematical text is simpler in some respects
We evaluate our translation system on both whole LATEX documents and a small test corpus of mathematical sentence pairs, and perform ablation testing to evaluate the importance of different components of our system
Summary
Machine translation for specialized domains such as legal or medical text has received considerable attention. Advances in these areas have been useful in practice and have given rise to new techniques in areas including domain adaptation [4], automatic term extraction [25] and domain-aware approaches to general-purpose machine translation [2]. The domain of mathematical text has, to our knowledge, not yet been the subject of research in machine translation, beyond some very early work [14] [17], we mention extensive ongoing research in the related areas of mathematical ontology and semantics [31], translation from informal mathematical writing into formal mathematics [29], and mathematical information retrieval [10]
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