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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 em- bedding 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 represent- ing 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 for- mulas 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.
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DPRL Systems in the CLEF 2020 ARQMath Lab
This paper describes the participation of the Document and Pattern Recognition Lab from the Rochester Institute of Technology in the CLEF 2020 ARQMath lab. There are two tasks defined for ARQMath: (1) Question Answering, and (2) Formula Retrieval. Four runs were submitted for Task 1 using systems that take advantage of text and formula embeddings. For Task 2, three runs were submitted: one uses only formula embedding, another uses formula and text embeddings, and the final one uses formula embedding followed by re-ranking results by tree-edit distance. The Task 2 runs yielded strong results, the Task 1 results were less competitive.
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- Award ID(s):
- 1717997
- PAR ID:
- 10198749
- Date Published:
- Journal Name:
- Working Notes of CLEF 2020 - Conference and Labs of the Evaluation Forum
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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