We tackle the problem of neural machine translation of mathematical formulae
between ambiguous presentation languages and unambiguous content languages.
Compared to neural machine translation on natural language, mathematical
formulae have a much smaller vocabulary and much longer sequences of symbols,
while their translation requires extreme precision to satisfy mathematical
information needs. In this work, we perform the tasks of translating from LaTeX
to Mathematica as well as from LaTeX to semantic LaTeX. While recurrent,
recursive, and transformer networks struggle with preserving all contained
information, we find that convolutional sequence-to-sequence networks achieve
95.1% and 90.7% exact matches, respectively.

本论文的主要研究方向是解决神经机器翻译数学公式的问题，特别是涉及到模糊表示语言和明确内容语言之间的翻译，论文采用卷积序列到序列网络来翻译 LaTeX 和 Mathematica，达到了 95.1% 和 90.7% 的准确匹配。

数学公式的神经机器翻译

Neural Machine Translation for Mathematical Formulae

Mathematical formulae represent complex semantic information in a concise
form. Especially in Science, Technology, Engineering, and Mathematics,
mathematical formulae are crucial to communicate information, e.g., in
scientific papers, and to perform computations using computer algebra systems.
Enabling computers to access the information encoded in mathematical formulae
requires machine-readable formats that can represent both the presentation and
content, i.e., the semantics, of formulae. Exchanging such information between
systems additionally requires conversion methods for mathematical
representation formats. We analyze how the semantic enrichment of formulae
improves the format conversion process and show that considering the textual
context of formulae reduces the error rate of such conversions. Our main
contributions are: (1) providing an openly available benchmark dataset for the
mathematical format conversion task consisting of a newly created test
collection, an extensive, manually curated gold standard and task-specific
evaluation metrics; (2) performing a quantitative evaluation of
state-of-the-art tools for mathematical format conversions; (3) presenting a
new approach that considers the textual context of formulae to reduce the error
rate for mathematical format conversions. Our benchmark dataset facilitates
future research on mathematical format conversions as well as research on many
problems in mathematical information retrieval. Because we annotated and linked
all components of formulae, e.g., identifiers, operators and other entities, to
Wikidata entries, the gold standard can, for instance, be used to train methods
for formula concept discovery and recognition. Such methods can then be applied
to improve mathematical information retrieval systems, e.g., for semantic
formula search, recommendation of mathematical content, or detection of
mathematical plagiarism.

分析了语境对公式信息转换的影响，提出了一种考虑语境的新方法，并提供了可用于公式信息提取训练等的基准数据集。