# Neural Machine Translation for Mathematical Formulae

arXiv: https://arxiv.org/abs/2305.16433 · HTML: https://mlsanity.com/paper/2305.16433/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Google's Multilingual Neural Machine Translation System: Enabling Zero-Shot Translation](https://mlsanity.com/paper/1611.04558/) (2016)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Pay Less Attention with Lightweight and Dynamic Convolutions](https://mlsanity.com/paper/1901.10430/) (2019)
- [Scaling Neural Machine Translation](https://mlsanity.com/paper/1806.00187/) (2018)
- [Image-to-Markup Generation with Coarse-to-Fine Attention](https://mlsanity.com/paper/1609.04938/) (2016)
- [Learning Longer-term Dependencies in RNNs with Auxiliary Losses](https://mlsanity.com/paper/1803.00144/) (2018)
- [First Experiments with Neural Translation of Informal to Formal Mathematics](https://mlsanity.com/paper/1805.06502/) (2018)
- [A Fast Unified Model for Parsing and Sentence Understanding](https://mlsanity.com/paper/1603.06021/) (2016)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Multilingual Neural Machine Translation with Task-Specific Attention](https://mlsanity.com/paper/1806.03280/) (2018)
- [Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context](https://mlsanity.com/paper/1804.04956/) (2018)
- [Discovering Mathematical Objects of Interest -- A Study of Mathematical Notations](https://mlsanity.com/paper/2002.02712/) (2020)
- [Semantic Preserving Bijective Mappings for Expressions involving Special Functions in Computer Algebra Systems and Document Preparation Systems](https://mlsanity.com/paper/1906.11485/) (2019)
- [Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources](https://mlsanity.com/paper/1505.01431/) (2015)
- [Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems](https://mlsanity.com/paper/2109.08655/) (2021)

## Built on by (most cited first, 7 of 7)

- [Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitions](https://mlsanity.com/paper/2502.12065/) (2025)
- [Multi-Operational Mathematical Derivations in Latent Space](https://mlsanity.com/paper/2311.01230/) (2023)
- [MASA: LLM-Driven Multi-Agent Systems for Autoformalization](https://mlsanity.com/paper/2510.08988/) (2025)
- [Empowering AI to Generate Better AI Code: Guided Generation of Deep Learning Projects with LLMs](https://mlsanity.com/paper/2504.15080/) (2025)
- [MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training](https://mlsanity.com/paper/2502.20855/) (2025)
- [English to Arabic machine translation of mathematical documents](https://mlsanity.com/paper/2312.03753/) (2023)
- [MioFFAn: an Annotation Software for Formula Formalization with LLM Automation Capabilities](https://mlsanity.com/paper/2607.22552/) (2026)

## Abstract (arXiv)

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.