### Abstract

When searching for mathematical content, accurate measures of formula similarity can help with tasks such as document ranking, query recommendation, and result set clustering. While there have been many attempts at embedding words and graphs, formula embedding is in its early stages. We introduce a new formula embedding model that we use with two hierarchical representations, (1) Symbol Layout Trees (SLTs) for appearance, and (2) Operator Trees (OPTs) for mathematical content. Following the approach of graph embeddings such as DeepWalk, we generate tuples representing paths between pairs of symbols depth-first, embed tuples using the fastText n-gram embedding model, and then represent an SLT or OPT by its average tuple embedding vector. We then combine SLT and OPT embeddings, leading to state-of-the-art results for the NTCIR-12 formula retrieval task. Our fine-grained holistic vector representations allow us to retrieve many more partially similar formulas than methods using structural matching in trees. Combining our embedding model with structural matching in the Approach0 formula search engine produces state-of-the-art results for both fully and partially relevant results on the NTCIR-12 benchmark. Source code for our system is publicly available.

Original language | English (US) |
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Title of host publication | ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval |

Publisher | Association for Computing Machinery, Inc |

Pages | 11-18 |

Number of pages | 8 |

ISBN (Electronic) | 9781450368810 |

DOIs | |

Publication status | Published - Sep 23 2019 |

Event | 9th ACM SIGIR International Conference on the Theory of Information Retrieval, ICTIR 2019 - Santa Clara, United States Duration: Oct 2 2019 → Oct 5 2019 |

### Publication series

Name | ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval |
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### Conference

Conference | 9th ACM SIGIR International Conference on the Theory of Information Retrieval, ICTIR 2019 |
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Country | United States |

City | Santa Clara |

Period | 10/2/19 → 10/5/19 |

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### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Information Systems

### Cite this

*ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval*(pp. 11-18). (ICTIR 2019 - Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval). Association for Computing Machinery, Inc. https://doi.org/10.1145/3341981.3344235